To evaluate the expression \( 4a + 6b \) when \( a = 2 \) and \( b = 1 \), we can substitute the values of \( a \) and \( b \) into the expression:
\[ 4a + 6b = 4(2) + 6(1) \]
Now, calculate each term:
\[ 4(2) = 8 \] \[ 6(1) = 6 \]
Adding these together:
\[ 8 + 6 = 14 \]
Thus, the value of the expression \( 4a + 6b \) when \( a = 2 \) and \( b = 1 \) is \( \boxed{14} \).