Solve -6m-6+8m=-5+2m-1 tell whether the equation has infinitely many solutions or no solutions

The first thing to do to solve -6m-6+8m=-5+2m-1, you must combine all of your like terms. This would look like this:
-6+2m=-6+2m

However, notice that after combining the like terms, your equations that are set equal to each other are the same. This means that the solutions to your equation are infinite, which would be your answer. 

The reason for this is if you were to continue trying to solve for m (subtracting both sides by 2m) you would result with this mathematical statement:
-6=-6

Because it is true, it signifies that any solution would work, meaning your equation has infinitely  many solutions.