This has to do with dot products (I can't make the arrow above the u, i, or j).

Given u = 4i - 6j and v = -3i + 5j, find 4u-(1/2)v

Am I just supposed to plug in what u and v are equal to in 4u-(1/2)v? If so, is the answer (35/2i - 53/2j)

looks good to me.

Yep, just do a scalar multiply on u,v and add the i,j values separately.