To solve the linear equation rac{2}{3}(3m - 6) = 5 - m, apply the general five-step strategy:

Step 1. Simplify both sides. Distribute the rac{2}{3} into the parentheses on the left side. The product of rac{2}{3} and $3m$ simplifies to $2m$, and rac{2}{3} times $-6$ simplifies to $-4$: $2m - 4 = 5 - m$

Step 2. Collect all variable terms on one side. Add $m$ to both sides to bring the variables to the left side: $2m + m - 4 = 5 - m + m$ $3m - 4 = 5$

Step 3. Collect all constant terms on the other side. Add $4$ to both sides to bring the constants to the right side: $3m - 4 + 4 = 5 + 4$ $3m = 9$

Step 4. Make the coefficient of the variable term equal to 1. Divide both sides by $3$: rac{3m}{3} = rac{9}{3} $m = 3$

Step 5. Check the solution. Substitute $3$ for $m$ in the original equation: rac{2}{3}(3(3) - 6) = 5 - 3 rac{2}{3}(9 - 6) = 2 rac{2}{3}(3) = 2 $2 = 2$

Since the equation balances, the solution $m = 3$ is correct.