Determine the changekf−ki in the kinetic energy of the block as it moves from xi = -6.00cm to xf = 4.00cm .

You can determine the change of kinetic energy by calculating the work done on the system. That would be force multiplied with distance. However, you only have the distance for the given. Anyway, I've found a similar problem. So, I hope I could still help you in understanding it, even just the concept.

So, in the similar problem that I found, two opposite forces are acting on a block along the frictionless surface. F1 = +80 N and F2 = -30 N.

We get the net force. Then, we find the work which is just kinetic energy in form.

W = KE = F*d
KE = (80 - 30)*(4 - -6)
KE = 500 J

So, if you have the actual values and direction of forces, the same concept applies. I hope I was able to help.