2/3 of 1¾ is simply their product, let's firstly convert the mixed fraction to improper fraction.
[tex]\bf \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\\\ \cfrac{2}{3}\cdot \cfrac{7}{4}\implies \cfrac{2}{4}\cdot \cfrac{7}{3}\implies \cfrac{1}{2}\cdot \cfrac{7}{3}\implies \cfrac{7}{6}\implies 1\frac{1}{6}[/tex]
