Everywhere you see an x, replace it with 2 to get

f(2) = 2^{5} - 11(2)^{4} + 18(2)^{3} -2(2) -200 2 to the 5th power is 32, 2 to the 4th is 16, 2 cubed is 8

=32 - 176 + 144 - 4 -200

f(2) = -204

but you asked to do it with synthetic division

divide x-2 into f(x) and you get x^{4}+9x^{3}-2 plus a remainder of -204 The remainder is your solution

The divisor is x-2. Take the 2 from f(2) and put a negative sign in front of it, added to x.

Then do the synthetic division much like you'd do any long division, only you have variables, not just numbers.

Getting the same answer 2 different ways suggests it's probably correct.