You can put this solution on YOUR website! What the problem is really asking you to do is to find the value of k such that both quadratic equations would have a root -4.
Find k such that
(-4)^2+(-4)-(2k+2) = 0
2*(-4)^2+k*(-4)-12 = 0
these are simple linear equations, solve them, I hope that I got them right.