let's first off, convert the mixed fraction to improper fraction, and then let's use the LCD of all denominators to do away with the denominators.
[tex]\bf \stackrel{mixed}{8\frac{1}{3}}\implies \cfrac{8\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{25}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{3}y+\cfrac{4}{5}=\cfrac{9}{10}\implies \stackrel{\textit{multiplying both sides by }\stackrel{\textit{LCD}}{30}}{30\left( \cfrac{25}{3}y+\cfrac{4}{5} \right)=30\left( \cfrac{9}{10} \right)}\implies 10\cdot 25y+6\cdot 4=3\cdot 9 \\\\\\ 250y+24=27\implies 250y=3\implies y=\cfrac{3}{250}[/tex]
