jmc

Note that $0.8\overline{4}=0.8+0.0\overline{4}$ and $0.\overline{4}=0.4+0.0\overline{4}.$ Our expression becomes $$\begin{array}{rl}0.8\overline{4}-0.\overline{4}& =(0.8+0.0\overline{4})-(0.4+0.0\overline{4})\\ & =0.8+0.0\overline{4}+(-0.4)+(-0.0\overline{4})\\ & =[0.8+(-0.4)]+[0.0\overline{4}+(-0.0\overline{4})]\\ & =0.4+0=\mathrm{0.4.}\end{array}$$The decimal number $0.4$, when expressed as a fraction, is $\frac{4}{10}=\boxed{\frac{2}{5}}.$