Confusion about the usage of hěn
There are two things that need to be aware of here.


The Chinese word 是(shi) is NOT equivalent to English "is/am/are". The Chinese 是(shi) functions as a "=". So both sides of the equal sign should have the same nature. So "ni shi mang" doesn't make sense.
A Chinese adjective is also a verb! That is, "mang" is already "to be busy"; "pretty" is already "to be pretty". Literally "you are busy" is "ni mang". But "hen" should be added to balance the rhythm of the sentence, and it isn't necessary to mean "very". So, the right sentence is "ni hen mang".


Finally, if you want to emphasize "very busy", it can be "ni fei chang mang".