You seem to have .. g(x) = {(2x^2 -4x -16)/(x -4) . . . x ≠ 4 .. .. .. .. ..{ kx -16 . . . . . . . . . . . . . . x=4
The first expression can be simplified to .. (2x^2 -4x -16)/(x -4) = 2(x +2)(x -4)/(x -4) = 2(x +2) . . . . x ≠ 4 At x=4, this simplified version has the value .. 2(4 +2) = 12
To make the alternate definition of g(x) have that same value at x=4, we must have .. k*4 -16 = 12 .. 4k = 28 ,, k = 7
The constant k must be 7 for the function to be continuous at x=4.