Hello Hazem, Since by using "understanding" you mean sympathetic, any of the synonyms below would work: compassionate, sympathetic, sensitive, considerate, kind, kindly, kindhearted, thoughtful, tolerant, patient, lenient, merciful, forgiving, humane, human, good-natured, approachable, supportive, reassuring, tactful, diplomatic, perceptive

In this context, "compensate" is equivalent to "make up." The sense here is "... I did my best to do extra work to compensate [for the work that I didn't do at other times]..."

You can use "compensate" or "recompense".