1. Stating the problem: Find the value of $y$ for the function $y = u(u^2 + 3)^3$ when $u = (x + 3)^2$ and $x = -2$. 2. Substitute $x = -2$ into $u = (x + 3)^2$: $$u = (-2 + 3)^2 = 1^2 = 1$$ 3. Substitute $u = 1$ into $y = u(u^2 + 3)^3$: $$y = 1(1^2 + 3)^3 = 1(1 + 3)^3 = 1 \times 4^3$$ 4. Calculate $4^3$: $$4^3 = 4 \times 4 \times 4 = 64$$ 5. Therefore, $$y = 1 \times 64 = 64$$ Final answer: $y = 64$