Let's simplify the expressions one by one:

12 3/5 - 7 1/6 + 2 3/10
Convert mixed numbers to improper fractions:
= (63/5) - (43/6) + (23/10)
Find a common denominator to simplify:
= (126/10) - (43/6) + (69/10)
= 12.6 - 7.16 + 6.9
= 3.14

2 2/3 + 3 1/2
Convert mixed numbers to improper fractions:
= (8/3) + (7/2)
Find a common denominator to simplify:
= (16/6) + (9/6)
= 25/6
= 4 1/6

170 8/51 - 2 4/9 ÷ 3 2/3
Convert mixed numbers to improper fractions:
= (8678/51) - (22/9) ÷ (11/3)
= (8678/51) - (22/9) * (3/11)
= (8678/51) - (6/11)
Find a common denominator to simplify:
= (160728/918) - (306/918)
= (160422/918)
= 174 230/918
= 174 115/459

Therefore, the final answer is 174 115/459.