Давайте решим по частям:

Сначала выразим все числа в виде обыкновенных дробей:
6 = 6/1
13/24 = 13/24
14 7/24 = (2414 + 7)/24 = 337/24
10 31/48 = (4810 + 31)/48 = 511/48
2 3/4 = (42 + 3)/4 = 11/4
1 7/12 = (121 + 7)/12 = 19/12
1 1/16 = (16*1 + 1)/16 = 17/16

Теперь решим пример:
6/1 - ((337/24) - (511/48) - (11/4 - 19/12)) - 17/16 =
= 6/1 - (337/24 - 511/48 - (11/4 - 19/12)) - 17/16 =
= 6/1 - (337/24 - 511/48 - (33/12 - 19/12)) - 17/16 =
= 6/1 - (337/24 - 511/48 - 14/12) - 17/16 =
= 6/1 - (337/24 - 511/48 - 7/6) - 17/16 =
= 6/1 - (337/24 - 511/48 - 56/48) - 17/16 =
= 6/1 - (337/24 - 567/48) - 17/16 =
= 6/1 - (337/24 - 567/48) - 17/16 =
= 6/1 - (337/24 - 567/48) - 17/16 =
= 6/1 - (337/24 - 567/48) - 17/16 =
= 6/1 - ((1416 - 1134)/48) - 17/16 =
= 6/1 - (282/48) - 17/16 =
= 6 - 5 7/16 =
= 0 9/16

Итак, 6 13/24 - ((14 7/24 - 10 31/48)-(2 3/4- 1 7/12))- 1 1/16 = 0 9/16.