If 4 - 3 + 5 = -6 + 8 + 4 is a mathematically correct statement, then both sides should end up with the same number:
4 - 3 + 5 = -6 + 8 + 4 Original statement.
1 + 5 = -6 + 8 + 4 You can do this in any order, but I start by doing the 4 - 3.
6 = -6 + 8 + 4 Finish simplifying the left side.
6 = 2 + 4 Combine the -6 and 8.
6 = 6 Finish simplifying the right side.
Because both sides are equal to each other, the sentence must be true.
Therefore, the sentence is true because when simplified, the statement is 6 = 6.
Hope this helps! :)
EDIT: Just incase anyone is curious, both this way and the way the other guy used both work, as they both prove that both sides are equal.