You just need to use $P_1$, $P_2$, $P_3$ and $Leftrightarrow$ symbols, for example $P_2$ is a formula, $(P_1 Leftrightarrow P_3) Leftrightarrow P_2$ is a formula. As stated in the question, you must not use $vee$, $wedge$ or $neg$.

You need to find the number of non-equivalent formulae. For example, $P_1$ is equivalent to $P_1Leftrightarrow P_1$, but $P_1Leftrightarrow P_2$ is not equivalent to $P_1 Leftrightarrow P_3$.