First, let's simplify the expression inside the parentheses:
12 13/20 - (86 9/20 - 24 7/10 - 3 3/4 - 3) 2 2/5
= 12 13/20 - (86 9/20 - 24 7/10 - 3 3/4 - 3) 12/5
= 12 13/20 - (86 9/20 - 24 7/10 - 15/4 - 3) 12/5
= 12 13/20 - (86 9/20 - 24 7/10 - 60/10 - 3) 12/5
= 12 13/20 - (86 9/20 - 24 7/10 - 6 - 3) 12/5
= 12 13/20 - (86 9/20 - 24 7/10 - 9) 12/5
= 12 13/20 - (86 9/20 - 24 7/10 - 9) 12/5
= 12 13/20 - (86 9/20 - 24 7/10 - 9) 12/5
= 12 13/20 - (86 9/20 - 226 42/20 - 9) 12/5
= 12 13/20 - (-140 7/20 - 9) 12/5
= 12 13/20 - (-149 7/20) 12/5
= 12 13/20 + 149 7/20 12/5
= 12 13/20 + 745/4
= (1220+13)/20 + 745/4
= (240+13)/20 + 745/4
= 253/20 + 745/4
= (2534+745)/20
= (1012+745)/20
= 1757/20

Therefore, the answer is 1757/20 or 87 17/20.