Subtract:

$\dfrac{4}{9}$ from $\dfrac{-7}{8}$

To subtract one rational number from another, add the additive inverse of the rational number to be subtracted.

Subtracting $\dfrac{4}{9}$ from $\dfrac{-7}{8}$,

LCM of 8 and 9 = 72

$\dfrac{-7}{8} - \dfrac{4}{9} = \dfrac{(-7) \times 9 - 4 \times 8}{72} \\[1em] = \dfrac{-63 - 32}{72} \\[1em] = \dfrac{-95}{72} \\[1em] = -1\dfrac{23}{72}$

Hence, the required difference is $\mathbf{-1\dfrac{23}{72}}$.