Draw a Turing machine that decides the language of all words over the alphabet {a, b} that have an odd number of a’s and an odd number of b’s Does the question mean draw a Turing machine that takes input with any number of a's and any number of b's (eg. aaabbb, ab, abababab, etc.). The turing machine should only then accept or reject the input and should not be stuck in loop?

Example of a drawing to answer the question:
Yes. "Words over the alphabet $\Sigma=\{a,b\}$" means that the input can be any string containing $a$s and $b$s in any order, and "decide" means that the machine must halt (accept or reject) on every input, and not get into an infinite loop.