What is light, a wave or a particle or A wave-particle? What is light?
And how do we know that light is an electromagnetic wave?
I asked my teacher and he said that when you place a compass in light's path, the needle of the compass rotates. Which I think is not a valid answer and thats not what actually happens when we place a compass in path of a light.
 A: Your instructor is wrong, and you are right. Placing a compass needle in a light beam will not cause the needle to turn, the way it certainly will if you place that compass near a magnet or a piece of wire carrying an electrical current. This is because light beams do not generate electrical current flow or magnetic fields in space, to which a compass could possibly react, because the fields associated with light beams are changing far too rapidly and are too weak. The situation is more complicated, and goes something like this:
Light was thought to be distinct from the realm of electricity and magnets until the 1860's when Maxwell wrote down his four equations which described all the (known) interactions between electricity and magnets. Maxwell then noted that his equations contained the possibility of waves consisting of coupled electric and magnetic fields, and that by manipulating his equations he could actually solve for the speed at which those waves would travel through space.
He then discovered that the speed of these "electromagnetic waves" was exactly the speed of light, which was known fairly accurately at that time. This proved that visible light was fundamentally electromagnetic in nature, and it represented just a tiny slice of the whole electromagnetic wavelength spectrum- encompassing radio, microwaves, infrared, visible, ultraviolet, x-ray, and gamma radiation.
But the flow of light, consisting of photons of electromagnetic energy, is not deflected by electric or magnetic fields, and its passage does not create electric or magnetic fields either that a compass could detect.
This story and all the background details I have omitted here will be found in any high-school level physics textbook, of which there are literally hundreds of good examples available. A college-level text will contain all the math and lots more detail.
A: 
What is light? And how do we know that light is an electromagnetic wave?

Light is what is needed for our eyes to see, and until the coming of Maxwell, light and electricity and magnetism were two very different physics observations.  To start with electricity was known from rubbing stuff together and getting sparks. Magnetism was known from stones found in Magnesia in Asia Minor where it was seen that there was attraction and repulsion, and by the time of Maxwell electricity and magnetism had been studied in circuits, mathematics describing their behavior was governed by specific laws., but nobody had connected electricity and magnetism to light.
Then came Maxwell with his brilliant equations that tied up the previous laws in a system of differential equations, which, when studied showed solutions that fitted the behavior of light! It was then the electromagnetic waves modeled correctly light and we have the progress we see by the unification of two different phenomena.
This link has examples of the way the mathematics describes with electric and magnetic fields, light.
If you study further, there is more to this, because now we know that there exists quantum mechanics, a layer of mathematics  below the mathematics of Maxwell where light is composed of photons, which add up to give the classical electromagnetic light, mathematically too, but it needs a lot of graduate study to understand the mathematics. It works in describing the observations and data.

I asked my teacher and he said that when you place a compass in light's path, the needle of the compass rotates.

I think your teacher has given a confused recollection of the Crookes radiometer . Certainly a compass will not be affected like that.
In  answer to the title

What is light, a wave or a particle or A wave-particle?

Light is represented by the classical electromagnetic wave and it can shown that it is an emergent superposition of a very large number of particles called photons. See this double slit experiment one photon at a time, how it builds up the classical interference pattern of light,


. Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

A: Electromagnetic waves are solutions of the wave equation that we derive from Maxwell's equations. When we use Maxwell's equation to compute predictions of what we expect to see when making experimental observations with light, we see that the predictions agree with the observation. Therefore, we conclude that light is an electromagnetic wave.
The frequency of light is extremely high. Therefore, a compass needle cannot respond fast enough to react to the change in the magnetic field in light.
Light is absorbed and emitted in quantized bits of energy that we call photons. The probability distribution for the detection of such a photon is given by the modulus square of the wave function, which is also a solution of Maxwell's equations. So the wave function and an electromagnetic wave differs only in that the wave function is normalized.
A: Light is a range of frequency of electromagnetic waves which our eyes can detect.
Light consists of photons, which is a weightless particle. Light is a medium through which energy can be released.
A: This is the simplistic answer that I found useful when I was a kid.
It isn't strictly rigourous, but it was useful. (See also "All models are wrong, but some models are useful".)

Light is something (a "thing", a phenomenom, whatever) which has the property that:

*

*if you do a test that asks "Does this thing behave in this way, which particles behave in?", it will mostly say "Yes".

*and if you do a test that asks "Does this thing behave in that way, which waves behave in" it will also mostly say "Yes".


It isn't meaningfully either thing.
It isn't "a wave" (in any sense that can used to draw analogies with other waves)
And it isn't "a particle" (again, in any sense that you use to draw analogies with other particles).
It's just light. It has properties of both / either / whichever one you ask about.
