Could be either here. yr gwaith has the sense of (my, your...) 'usual work' as well as 'the work' meaning a particular piece of work.
as "gorau" means "best", I put "I should give the best at work" (i.e. I should always do my best). Having been marked wrong, I've now seen that "roi'r gorau i" means "to give up", but how would I translate: "I should give the best at work" into Welsh?