What should be subtracted from -2 to get $\dfrac{3}{8}$ ?

Let $x$ be subtracted from -2.

$-2 - x = \dfrac{3}{8}\\[1em] \Rightarrow \dfrac{-2}{1} - x = \dfrac{3}{8}\\[1em] \Rightarrow x = \dfrac{-2}{1} - \dfrac{3}{8}$

LCM of 1 and 8 is 2 x 2 x 2 = 8

$\Rightarrow x = \dfrac{-2 \times 8}{1 \times 8} - \dfrac{3 \times 1}{8 \times 1}\\[1em] \Rightarrow x = \dfrac{-16}{8} - \dfrac{3}{8}\\[1em] \Rightarrow x = \dfrac{-16 - 3}{8}\\[1em] \Rightarrow x = \dfrac{-19}{8}\\[1em] \Rightarrow x = -2 \dfrac{3}{8}$

The number subtracted from -2 to get $\dfrac{3}{8}$ is -$2\dfrac{3}{8}$.