How do you do this problem. Thanks for your help.

4(2m+3)=-3(m-1)+7

First, remove the parentheses using the distributive property of multiplication over addition:

4(2m+3)=-3(m-1)+7
4*2m + 4*3 = -3*m -3*(-1) + 7
8m + 12 = -3m +3+7
Collect unknowns on the left hand side, and constants on the right:
8m - (-3m) = 3+7-12
11m = -2
m=-2/11