$$5\frac{2}{3}a - a + 2\frac{1}{12}a = (5\frac{2}{3} - 1 + 2\frac{1}{12})a = (5\frac{8}{12} - 1 + 2\frac{1}{12})a = (4\frac{8}{12} + 2\frac{1}{12})a = 6\frac{9}{12}a = 6\frac{3}{4}a = \frac{27}{4}a$$
$$a = 1\frac{7}{9} = \frac{16}{9}$$
$$\frac{27}{4} \cdot \frac{16}{9} = \frac{27 \cdot 16}{4 \cdot 9} = \frac{3 \cdot 4}{1 \cdot 1} = 12$$
Ответ: 12