How is the wind pushing the crate left in this exercise, is the force applied is downwards and to the right? 
Taken from Fundamentals of Physics.
I understand the theory and the resolution. What I don't understand is how what is happening in the diagram is possible. How is it that the wind is pushing downwards and to the right on a crate and it somehow slides backwards? I figure it's something to do with Newton's 3rd law and how the floor pushes back on the crate with a force of $-F^\rightarrow$. If so why is there no vertical acceleration?
 A: The crate is said to be displaced. There isn't an explanation for why its displacement occurs. Obviously it was given some impulse ($F_{initial}\Delta t = m\Delta v$) which gave the crate enough kinetic energy to move 3 meters while experiencing the the opposing force exerted by the wind.
There's no Newton's third law explanation for its displacement ($\vec{d} = -3.0  m\, \hat{i} $) relating to the force exerted by the wind.
A: 
How is it that the wind is pushing downwards and to the right on a
  crate and it somehow slides backwards?

It's initially sliding backwards. The horizontal component of the wind to the right is simply slowing it down (reducing its backwards velocity).
The way I read the problem is the crate is initially sliding to the left, probably at constant velocity since it is implied that the surface is frictionless (an "oily" surface). The wind then blows down and to the right. The horizontal component of the wind force to the right causes the crate to decelerate, i.e., "slows it down" as indicated in the upper right caption in the diagram.
Hope this helps.
