Use the work-energy theorem for the entire process, from the compressed spring state to the final resting state. The initial energy is the elastic potential energy stored in the spring. This energy is entirely dissipated by the work done by friction over the total distance the block slides.

Initial energy: $E_i = E_{p,s} = \frac{1}{2}kx^2$ Final energy: $E_f = 0$ Work done by friction: $W_f = -f_k s_{total} = -\mu mg (x+d)$ The total sliding distance is $s_{total} = x+d$.

The change in mechanical energy equals the work done by non-conservative forces:

$$\Delta E = E_f - E_i = W_f$$ $$0 - \frac{1}{2}kx^2 = -\mu mg(x+d)$$

Solving for the coefficient of friction $\mu$:

$$\mu = \frac{kx^2}{2mg(x+d)}$$

Substituting values with $x = 0.15$ m, $d = 0.60$ m, and $g = 9.8$ m/s²:

$$\mu = \frac{(200 \text{ N/m})(0.15 \text{ m})^2}{2(2.0 \text{ kg})(9.8 \text{ m/s}^2)(0.15 \text{ m} + 0.60 \text{ m})} = \frac{4.5}{2(2.0)(9.8)(0.75)} = \frac{4.5}{29.4}$$