3/4:(6 целых 3/8 - y) = 8 целых 6/7

3/4 : (6 3/8 - y) = 8 6/7; 

6 3/8 - у = 3/4 : 8 6/7; 

6 3/8 - у = 3/4 : 62/7; 

6 3/8 - у = 3/4 * 7/62; 

6 3/8 - у = (3 * 7) / (4 * 62); 

6 3/8 - у = 21/248; 

у = 6 3/8 - 21/248; 

у = 51/8 - 21/248; 

у = (51 * 31) / (8 * 31) - 21/248; 

у = 1581/248 - 21/248; 

у = 1560/248; 

у = 195/31; 

у = 6 9/31. 

Проверка: 

3/4 : (6 3/8 - 6 9/31) = 8 6/7;

3/4 : (51/8 - 195/31) = 8 6/7; 

3/4 : ((51 * 31) / (8 * 31) - (195 * 8) / (31 * 8)) = 8 6/7; 

3/4: (1581/248 - 1560/248) = 8 6/7; 

3/4 : 21/248 = 8 6/7; 

3/4 * 248/21 = 62/7; 

(3 * 248) / (4 * 21) = 62/7; 

744/84 = 62/7; 

62/7 = 62/7. 

Решение верно.