To find \( f(1) \) using the function rule \( f(x) = 4(12)^x + 4 \), we substitute \( x = 1 \) into the expression.
\[ f(1) = 4(12)^1 + 4 \]
Calculating \( (12)^1 \):
\[ (12)^1 = 12 \]
Now substitute this value back into the expression:
\[ f(1) = 4 \cdot 12 + 4 \]
Calculating \( 4 \cdot 12 \):
\[ 4 \cdot 12 = 48 \]
Now, add 4:
\[ f(1) = 48 + 4 = 52 \]
So, the value of \( f(1) \) is
\[ \boxed{52} \]