[tex]remining\ gallons\ of\ water= water\ filled-\ water\ which\laked\ out\\\\
remining\ gallons\ of\ water=6\frac{1}{2}-2\frac{5}{6}=6\frac{3}{6}-2\frac{5}{6}=\\\\5\frac{9}{6}-2\frac{5}{6}=3\frac{4}{6}=3\frac{2}{3}\\\\In\ the\ cooler\ remained\ 3\frac{2}{3}gallons\ of\ water.[/tex]