$X$ & $Y$ are two subspaces of $W$. Show $(X+Y)/Y$ is isomorphic to $X/(X∩Y)$.
So to show that I believe I have to show a bijective homomorphism of linear spaces $ T: W\to V$. Now there is the theorem: Two finite-dimensional vector spaces over a field are isomorphic if and only if they have the same dimension.
So to find a basis for each of the vector space & count the elements, I would assume $X$ & $Y$ have $x$ & $y$ elements respectively? Then show that the two bases have the same number of elements by counting the bases of $(X+Y)/Y$ which I am a little unsure about.
How about defining a linear map $L: X\to \frac{X+Y}{Y}$ via $L(x)=x+Y$?
Is $L$ surjective? What is the kernel of $ L$?