Automa that can recognize any given DNA sequence

Question

I'm new here, I'm on my first year of college for computer science, and I have my final exam for logic in 3 days. One of the question that the teacher could ask me is to design an Automa that can recognize any given sequence of DNA, so all the different permutations of the set {a,c,g,t}. And honestly Idk where to start. I'm not using any programming language so it's all about theory, if anyone could explain to me the logic behind an automa that can recognize permutations of a set, that would be great. Thanks in advance