* άσχολος (áscholos): This is probably the closest single word. It implies being occupied, engaged, or preoccupied with something. It often carries a connotation of being seriously involved or even burdened.
* απασχολημένος (apascoliménos): This is the participle form of απασχολώ (apascholó), meaning "to occupy" or "to keep busy." It's a more formal and passive way of saying "busy."
* πλήρης εργασίας (plíris ergasias): This translates literally to "full of work," and is a more descriptive phrase.
The best choice will depend on the context. If you can provide the sentence you're trying to translate, I can give you a more precise suggestion.