To find the value of the expression \(2w + 4(w + 3s)\) when \(w = 4\) and \(s = 2\), we can substitute the values of \(w\) and \(s\) into the expression.
- Substitute \(w = 4\) and \(s = 2\) into the expression:
\[ 2w + 4(w + 3s) \]
becomes
\[ 2(4) + 4(4 + 3(2)) \]
- Calculate \(2(4)\):
\[ 2(4) = 8 \]
- Calculate \(3(2)\):
\[ 3(2) = 6 \]
- Now substitute back into the expression:
\[ 4(4 + 6) = 4(10) = 40 \]
- Combine the results:
\[ 8 + 40 = 48 \]
Thus, the value of the expression \(2w + 4(w + 3s)\) when \(w = 4\) and \(s = 2\) is \(\boxed{48}\).