Synthetic division is a shortcut for dividing polynomials of the form x-a among others. It looks like long division by a, except there are no carries and we add instead of subtract.
This one tells us
By the polynomial remainder theorem, that remainder of 14 is f(4). Let's check it
Wow, math works.
For part 2, it's a bit of a trick question. When f(x) is divided by x-3 the remainder will be f(3) not f(-3).
That doesn't really tell us anything about f(-3); we'd have to evaluate it or divide by x+3 to make sure it isn't 15, but it very likely isn't.
I'll assume by separate problem they mean a different, unspecified f.