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 <em>Original statement.</em>
1 + 5 = -6 + 8 + 4 <em>You can do this in any order, but I start by doing the 4 - 3.</em>
6 = -6 + 8 + 4 <em>Finish simplifying the left side.</em>
6 = 2 + 4 <em>Combine the -6 and 8.</em>
6 = 6 <em>Finish simplifying the right side.</em>
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.
<em>Hope this helps! :)</em>
<u><em>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.</em></u>