To simplify the expression \(10(2m+6)\) using the distributive property, you multiply the term outside the parentheses by each term inside the parentheses.
Here's how it looks:
\[ 10(2m + 6) = 10 \cdot 2m + 10 \cdot 6 \]
Now, perform the multiplication:
\[ = 20m + 60 \]
So, the simplified expression is:
\[ 20m + 60 \]