To simplify the expression \(2 \cdot (2 + 3a)\), you can distribute the \(2\) into the parentheses:
\[ 2 \cdot (2 + 3a) = 2 \cdot 2 + 2 \cdot 3a \]
Calculating each term:
\[ 2 \cdot 2 = 4 \]
\[ 2 \cdot 3a = 6a \]
Putting it all together, we have:
\[ 2 \cdot (2 + 3a) = 4 + 6a \]
So the simplified expression is:
\[ 4 + 6a \]