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f(4+h) - f(4)

solve it in two parts

part1: f(4+h) and then part2: f(4) when you have both, subtract part 2 from part 1

part1: x= 4+h

so f(x) = x^2 - 2 = (4+h)^2 - 2 = 4^2 + 8h + h^2 - 2 = 16 + 8h + h^2 -2 = h^2 + 8h +14

part2: x = 4

f(x) = x^2 - 2 = 4^2 - 2 = 16 -2 = 14

f(4+h) - f(4) = (h^2 + 8h + 14) - (14) = h^2 + 8h