1. **Problem statement:** A wheel starts from rest and accelerates with an angular acceleration $a = 4$ rad/s$^2$. We need to find how many revolutions it makes in 6 seconds. 2. **Relevant formula:** The angular displacement $\theta$ (in radians) under constant angular acceleration starting from rest is given by: $$\theta = \frac{1}{2} a t^2$$ where $a$ is angular acceleration and $t$ is time. 3. **Calculate angular displacement:** $$\theta = \frac{1}{2} \times 4 \times 6^2 = 2 \times 36 = 72 \text{ radians}$$ 4. **Convert radians to revolutions:** One revolution corresponds to $2\pi$ radians, so the number of revolutions $N$ is: $$N = \frac{\theta}{2\pi} = \frac{72}{2\pi} = \frac{72}{6.2832} \approx 11.46$$ 5. **Interpretation:** The wheel makes approximately 11.46 revolutions in 6 seconds. **Final answer:** C. 11.46 rev