What is the regular expression to the given language?
Look at the three parts of your language:


For the $a^{3k-1}$ part, we have possibilities $a^2, a^5, a^8, \dots$. For this part we'll have any 2 $a$s plus a multiple of 3 $a$s. That's expressible as $aa(aaa)^*$.
The $b^n$ part is easy, it's just $b^+$, since you need $n&gt;0$.
The $a^{2t}$ part is likewise easy. Since $t\ge 1$ we can express this as $(aa)^+$.


Now concatenate these three regular expressions.