Vector Algebra: JEE Main 2023 Mathematics question

Let $\overrightarrow a$, $\overrightarrow b$ and $\overrightarrow c$ be three non zero vectors such that $\overrightarrow b$ . $\overrightarrow c$ = 0 and $\overrightarrow a \times (\overrightarrow b \times \overrightarrow c ) = {{\overrightarrow b - \overrightarrow c } \over 2}$. If $\overrightarrow d$ be a vector such that $\overrightarrow b \,.\,\overrightarrow d = \overrightarrow a \,.\,\overrightarrow b$, then $(\overrightarrow a \times \overrightarrow b )\,.\,(\overrightarrow c \times \overrightarrow d )$ is equal to