15÷4 × 2⅔÷⅚×3÷10

$2\frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6+2}{3} = \frac{8}{3}$

$15 \div 4 \times \frac{8}{3} \div \frac{5}{6} \times 3 \div 10$

$15 \times \frac{1}{4} \times \frac{8}{3} \times \frac{6}{5} \times 3 \times \frac{1}{10}$

$\frac{15 \times 1 \times 8 \times 6 \times 3 \times 1}{4 \times 3 \times 5 \times 10}$

$\frac{15}{5 \times 3} = 1$
$\frac{8}{4} = 2$
$\frac{6}{10} = \frac{3}{5}$

The expression becomes:
$1 \times \frac{1}{1} \times 2 \times \frac{3}{5} \times 3 \times \frac{1}{1}$

$\frac{1 \times 1 \times 2 \times 3 \times 3 \times 1}{1 \times 1 \times 1 \times 5 \times 1 \times 1} = \frac{18}{5}$

$\frac{18}{5} = 3\frac{3}{5}$ or 3.6