How to solve this circuit?

Interesting question. Here is how I would approach it:

1) Load Power (P) = V(load)^2/R(load)
2) V(load) = 15V - 6kohm [ I2 + I(load) - 5mA]
3) I2 = V(load)/2kohm
4) I(load)= V(load)/R(load)

You can use (3) and (4) to substitute into (2) and solve for V(load) as a function of R(load). Substitute that into (1) and you have a function for P in terms of R(load). Solve the resulting equation for the maximum value.