To find \( g(f(0)) \), we first need to calculate \( f(0) \).
Given the function \( f(x) = 2x + 1 \), we substitute \( x = 0 \):
\[ f(0) = 2(0) + 1 = 1 \]
Now we have \( f(0) = 1 \). Next, we need to find \( g(f(0)) = g(1) \).
Now, using the function \( g(x) = 4x \), we substitute \( x = 1 \):
\[ g(1) = 4(1) = 4 \]
So, \( g(f(0)) = 4 \).
The answer is \( \boxed{4} \).