dwywaith (ddwywaith when used as an adverb) would normally translate as 'twice'. If you specifically wanted to say 'two times', as in 'on two particular occasions', it might be better to use dwy waith (two times) or ar ddau achlysur (on two occasions).
I'm not sure how "two times" differs from "twice"? Perhaps it's coming from an American English perspective, but I can't think of an example when twice would not mean either two particular occasions (I broke my arm twice) except for the British English way of doing multiplication (twice four is eight) - which Americans invariably use "times" for (two times four is eight). Can you help me understand the difference - when would twice be an adjective that doesn't mean two times - with an example?
''Two times' is now an accepted answer. Bear in mind that you would not use it for 'two times' as in something like 'The two times that I went to the gallery it was closed'.