1. **State the problem:** We need to find the value of $f(-2 - g(3))$ given the functions $f(x) = \frac{3}{4}x + 10$ and $g(x) = x^2 - 3$. 2. **Calculate $g(3)$:** Substitute $x=3$ into $g(x)$: $$g(3) = 3^2 - 3 = 9 - 3 = 6$$ 3. **Evaluate the expression inside $f$:** $$-2 - g(3) = -2 - 6 = -8$$ 4. **Calculate $f(-8)$:** Substitute $x = -8$ into $f(x)$: $$f(-8) = \frac{3}{4}(-8) + 10$$ 5. **Simplify the multiplication:** $$f(-8) = \frac{3}{4} \times -8 + 10 = \cancel{\frac{3}{4}} \times \cancel{-8} \times -2 + 10 = -6 + 10$$ 6. **Final calculation:** $$f(-8) = 4$$ **Answer:** The value of $f(-2 - g(3))$ is $4$.