Let $P$ be a normal, $\mathbb{Q}$-Gorestein variety with terminal singularities. Let $X \subseteq P$ be a normal, irreducible Weil divisor such that $X \sim_{\mathbb{Q}} - K_P$, that is $\mathbb{Q}$-linearly equivalent to the anticanonical divisor of $P$ (which is $\mathbb{Q}$-Cartier) .

My question is, does $X$ have $\mathbb{Q}$-trivial canonical divisor? In the adjuction formula for Weil divosr, it seems there is a $Diff$ term appears. I was wondering if this term is zero here?