1. **State the problem:** We are given two functions $f(x) = x + 9$ and $g(x) = 2x + 3$. We need to find the value of $f(g(3))$. 2. **Understand the composition:** The expression $f(g(3))$ means we first find $g(3)$, then plug that result into $f$. 3. **Calculate $g(3)$:** $$g(3) = 2(3) + 3 = 6 + 3 = 9$$ 4. **Substitute $g(3)$ into $f$:** $$f(g(3)) = f(9) = 9 + 9 = 18$$ 5. **Final answer:** $$\boxed{18}$$