In Step 3 of the given solving process, the operation performed is subtracting 12 from both sides of the equation:
\[ 6m + 12 - 12 = 5m + 7 - 12 \]
This shows that you are maintaining equality by subtracting the same value (12) from both sides of the equation. Therefore, the property of equality displayed in Step 3 is the Subtraction Property of Equality.