Step 1 :Assign values for $x$ and find the corresponding values of $f(x)$ from the given function.
Step 2 :First, find the value of $f(x)$ when $x=-3$
Step 3 :Substitute $x=-3$ into the function $f(x) = 2^{(x+1)}+4$
Step 4 :Calculate $f(-3) = 2^{-2}+4$
Step 5 :The value of $f(-3)$ is \(\boxed{4.25}\)