To simplify the expression \( 7(2x + 4) \) using the Distributive Property, we multiply \( 7 \) by each term inside the parentheses:
\[ 7(2x) + 7(4) \]
Now, calculate each multiplication:
\[ 7 \times 2x = 14x \] \[ 7 \times 4 = 28 \]
Putting it all together, we have:
\[ 7(2x + 4) = 14x + 28 \]
So, the simplified expression is:
\[ \boxed{14x + 28} \]