$\begin{array}{l} {\left( {\sin x - \cos x} \right)^2} = \dfrac{1}{2} \Rightarrow {\sin ^2}x + {\cos ^2}x - 2\sin x\cos x = \dfrac{1}{4} \Rightarrow \sin x\cos x = \dfrac{3}{8}\\ {\sin ^4}x + {\cos ^4}x = {\left( {{{\sin }^2}x + {{\cos }^2}x} \right)^2} - 2{\sin ^2}x{\cos ^2}x = 1 - 2.{\left( {\dfrac{3}{8}} \right)^2} = \dfrac{{23}}{{32}} \Rightarrow B \end{array}$