Can someone me describe and correct the error here? i was absent at school when we learned this but now im stuck doing the homework.

If you add 13 to each side, that wouldn't be correct because that is not how you get rid of the 13 that is being added to m. If you want m by itself, ask yourself : what is the opposite of adding 13 to x? It would be subtracting 13, to get 0, leaving m by itself. So if you subtracted 13 from that side, you have to subtract it to the other side, so then 56 subtracted by 13 would be 43. In conclusion,
x = 13. Hope this helps! Let me know if you still don't get it. Glad you're feeling better! :)