Выполним сложение:
$$6\frac{8}{9} + 3\frac{1}{12} = \frac{6 \cdot 9 + 8}{9} + \frac{3 \cdot 12 + 1}{12} = \frac{54 + 8}{9} + \frac{36 + 1}{12} = \frac{62}{9} + \frac{37}{12} = \frac{62 \cdot 4}{9 \cdot 4} + \frac{37 \cdot 3}{12 \cdot 3} = \frac{248}{36} + \frac{111}{36} = \frac{248 + 111}{36} = \frac{359}{36} = 9 \frac{35}{36}$$
Ответ: $$9 \frac{35}{36}$$