first off, we'd convert the mixed fractions to "improper", and then just get the product
[tex]\bf \stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}}
\\\\\\
\cfrac{2}{3}\cdot \cfrac{11}{4}\implies \cfrac{22}{12}\implies \cfrac{11}{6}\implies 1\frac{5}{6}[/tex]
