What is the conjugate acid of ClO4-?

Here's how you go about acid/base chemistry

The Bronsted-Lowry definition of an acid is a proton donator and a base is a proton acceptor. A proton is synonymous to a ##H^+## ion, so acid/ base chemistry is all about the ##H^+##.

We can observe that the ion you were given, ##ClO_4^_## has a one negative charge. meaning it has the capacity to accept on ##H^+##.

Therefore, its conjugate acid is ##HClO_4##. Notice the neutral charge and the presence of the ##H^+##. That's the giveaway you're looking for.

Hope that helps!