Finding a regular expression of a language
You have to put your triplets, and use Kleene star: $$(aaa)^*(bbb)^*$$

Now, add cases where number of $a$ is not divisible by 3, say aabbbb, as alternative.
$$ (aaa)^*(bbb)^* + (aaa)^*aab(bbb)^* + (aaa)^*abb(bbb)^*$$