Finite State Machines Help!

can anyone help me please ive an exam next week and i can’t seem to know how to construct a finite state machine .

L={b,aa,ba,aababaa,aaba,bbaba}

what should it do?
what progrmming language do you need help with?
have you already searched on the internet and found something?

What part confuses you? How far can you get on your own?