Translation:Chcę pokazać, że umiem liczyć.
So "mogę" instead of "umiem" won't work here?
It is about the ability you have learned, so "umiem"
Do "rachować" and "liczyć" mean the same?
Rachować means to calculate, to do calculations, to do (the) math(s)
Some nights I should not be doing this, this is one of them.