Can someone explain why a longitude wave can pass through the liquid, but a transverse wave can't. And can someone recommend some good animation of these processes.
To answer your question, first let's see how transverse waves or S-Waves propagate, so in simple terms we can state that, S-Waves or transverse are shear waves, whose particles move perpendicularly to their direction of propagation.
Now, let's see why can they propagate through solids. They can propagate through solid because solids have enough shear strength. The shear strength is one of the forces that hold the solid together, and prevent it from falling apart.
The case with liquids is that, liquids do not have that much shear strength: for example consider this, if you take a glass of water and suddenly, somehow you remove the glass, the water will not keep it's shape and will just flow away. So in fact it just boils down to the fact that transverse-waves need a medium rigid enough to propagate, which liquids can't provide.
Also remember that not all transverse waves require a rigid medium to travel. Transverse waves can also travel along the surface tension of the ocean, creating water waves. Light and electromagnetic waves are also transverse waves, however they are self-propagating, meaning that they sustain themselves due to the magnetic field they create, and thus can travel through a vacuum, only slowing down slightly when passing through water or air.
Hope it helps!