4 2/3 *6-1 23/42*3 1/3+2 1/8*1 29/51

Поочередно введем целые доли в дроби и произведем нужные по условию действия. Итак:

4 2/3 = (4 * 3 + 2)/3 = (12 + 2)/3 = 14/3;

1 23/42 = (42 * 1 + 23)/42 = (42 + 23)/42 = 65/42;

3 1/3 = (3 * 3 + 1)/3 = 10/3;

2 1/8 = (2 * 8 + 1)/8 = 17/8;

1 29/51 = (1 * 51 + 29)/51 = 80/51.

Сейчас умножение:

4 2/3 * 6 = 14/3 * 6 = 84/3;

1 23/42 * 3 1/3 = 65/42 * 10/3 = 65/21 * 5/3 = 325/63;

2 1/8 * 1 29/51 = 17/8 * 80/51 = 1/1 * 10/3 = 10/3.

Осталось вычитание и сложение:

84/3 - 325/63 + 10/3 = (21 * 84)/63 - 325/63 + (21 * 10)/63 =

= 1/63 * (21 * (84 + 10) - 325) = 1/63 * (21 * 94 - 325) =

= 1/63 * (94 * (20 + 1) - 325) = 1/63 * (1880 + 94 - 325) = 

1/63 * (1555 + 94) = 1649/63 = (1638 + 11)/63 = 1638/63 + 11/63 =

= 234/9 + 11/63 = (180 + 54)/9 + 11/63 = 20 + 6 + 11/63 = 26 11/63.

Ответ: 26 11/63.