Answer
The statement $p\leftrightarrow q$ means "p if and only if q". This statement evaluates to true only when $p$ and $q$ have the same truth value, so it is only true when both $p$ and $q$ are true or both $p$ and $q$ are false. The second proposition, $(p\land q)\lor(\neg p\land\neg q)$ means "p and q, or not p and not q". This too will evalueate to true only when both $p$ and $q$ are true or when $p$ and $q$ are both false. Since the two propositions have the same truth value for every truth assignment of $p$ and $q$, they are logically equivalent.
Work Step by Step
This question asked us for an explanation, so I included the full explanation in the answer section. Please see above.
