The right-hand limit simply means we approach the limit from the positive side, the right-hand side, of the curve.
(a) The right-hand side of the curve when x approaches -2 shoots off to infinity, so the answer is “infinite”.
(b) The curve is continuous at x=10 so the left- and right-hand limits are the same. At and near x=10 the curve crosses or approaches the x axis, and the x axis is f(x)=0. So the limit is 0, which happens to be f(10).