Can anyone pls me with this algebra question click to see a picture of the problem

The value of k is 6.

The vertex of f(x) is at (4, 1).  The vertex of g(x) is at (-2, 1).  It has been shifted left 6 units.  This means that the value of k must be -6 (when translating a function horizontally, the number we add/subtract is the opposite of what we would normally think; we think of left as negative, but to shift it left, we actually add).