First, find the value of $\ddot{f(x)}$ when $x=-3$ \[ \begin{aligned} f(-3) & =2^{(-3+1)+4} \\ & =2^{-2}+4 \\ & =\square \times-4 \\ & =\square \end{aligned} \]

Step 1 ：Substitute $x=-3$ into the function $f(x) = 2^{(x+1)} + 4$

Step 2 ：Simplify the expression to get $f(-3) = 2^{(-3+1)} + 4$

Step 3 ：Further simplify to get $f(-3) = 2^{-2} + 4$

Step 4 ：Calculate the value of $2^{-2}$ and add 4 to get $f(-3) = 0.25 + 4$

Step 5 ：Finally, simplify to get $f(-3) = 4.25$

Step 6 ：\(\boxed{4.25}\) is the final answer