Use the Remainder Theorem, which says that the value for x that makes the factor (in this case, x–k) equal to 0 can be substituted into the function to yield the remainder (in this case, 6).
In this case, k is the value that makes x–k have the value of 0. Thus, we will use k as the value of x in the function or polynomial given and then set that equal to the remainder, which was given to us as 6.
f(x) = x3 + 2xk – 3k [original function given to us]
f(k) = k3 + 2(k)(k) – 3 k = 6 [original function with k used as the value of x and the function set equal to 6, the remainder]
k3 + 2k2 – 3k = 6
I decided that trial and error was my quickest way to find k, but I'll let you find k however you choose.