To solve the expression (1 \frac{3}{5} + (4 - 2 \frac{12}{13})), we follow these steps:

Convert the mixed number (1 \frac{3}{5}) to an improper fraction:
[
1 \frac{3}{5} = \frac{5 \cdot 1 + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5}
]

Calculate (2 \frac{12}{13}):
[
2 \frac{12}{13} = \frac{13 \cdot 2 + 12}{13} = \frac{26 + 12}{13} = \frac{38}{13}
]

Substitute back into the expression:
[
4 - 2 \frac{12}{13} = 4 - \frac{38}{13}
]
Convert 4 to a fraction with a denominator of 13:
[
4 = \frac{4 \cdot 13}{13} = \frac{52}{13}
]
Now, we have:
[
\frac{52}{13} - \frac{38}{13} = \frac{52 - 38}{13} = \frac{14}{13}
]

Now, we add (\frac{8}{5}) and (\frac{14}{13}):
To do this, we need a common denominator. The least common multiple of 5 and 13 is 65.

Convert (\frac{8}{5}) to a denominator of 65:
[
\frac{8}{5} = \frac{8 \cdot 13}{5 \cdot 13} = \frac{104}{65}
]

Convert (\frac{14}{13}) to a denominator of 65:
[
\frac{14}{13} = \frac{14 \cdot 5}{13 \cdot 5} = \frac{70}{65}
]

Now, add (\frac{104}{65}) and (\frac{70}{65}):
[
\frac{104}{65} + \frac{70}{65} = \frac{104 + 70}{65} = \frac{174}{65}
]

Finally, simplify (\frac{174}{65}) if possible. (174) and (65) have no common factors other than (1).

Thus, the final answer is:
[
\frac{174}{65}
]

This can also be expressed as a mixed number:
[
\frac{174}{65} = 2 \frac{44}{65}
]

So, (1 \frac{3}{5} + (4 - 2 \frac{12}{13}) = \frac{174}{65}) or (2 \frac{44}{65}).