To find the value of \( g(20) \), we will substitute \( x = 20 \) into the function \( g(x) = 6(2x + 7) \).
First, substitute \( x \) with 20:
\[ g(20) = 6(2(20) + 7) \]
Now, calculate \( 2(20) \):
\[ 2(20) = 40 \]
Next, add 7 to this result:
\[ 40 + 7 = 47 \]
Now, multiply this sum by 6:
\[ g(20) = 6 \times 47 \]
Calculating that gives:
\[ 6 \times 47 = 282 \]
So, the value of \( g(20) \) is \( \boxed{282} \).