1. **State the problem:** Given the function equation $f(2x - 3) = 4x + 6$, find the expression for $f(x)$ and then evaluate $f(3)$. 2. **Understand the problem:** We have $f$ applied to the expression $2x - 3$. To find $f(x)$, we want to rewrite the input of $f$ in terms of a single variable, say $t$, where $t = 2x - 3$. 3. **Express $x$ in terms of $t$:** $$t = 2x - 3 \implies 2x = t + 3 \implies x = \frac{t + 3}{2}$$ 4. **Rewrite the given equation in terms of $t$:** $$f(t) = 4 \left( \frac{t + 3}{2} \right) + 6 = 2(t + 3) + 6 = 2t + 6 + 6 = 2t + 12$$ 5. **Therefore, the function $f$ is:** $$f(x) = 2x + 12$$ 6. **Evaluate $f(3)$:** $$f(3) = 2(3) + 12 = 6 + 12 = 18$$ **Final answers:** $$f(x) = 2x + 12$$ $$f(3) = 18$$