If x + 3 is a factor x^2 + kx + 2k, where k is a constant, what is the value of k?

What the statement means is that x^2 + kx + 2k = 0 when x = -3. That's because x + 3 will equal zero
(-3)^2 + (-3k) + 2k = 0
9 - 3k + 2k =0
9 - k = 0
9 =  k

Check

x^2 + 9x + 18 = 0
(x + 3)(x + 6) = 0
These are the two factors. As expected from the givens one of them is (x + 3)