If $795.60 represents 12% of Inga's monthly income, how much is 60% of Inga's monthly income?

Let Inga's monthly income be $x.

Since $795.60 represents 12% of Inga's monthly income, then we can set up the equation: 0.12x = $795.60.
Solving for x gives: x = $795.60 / 0.12 = $6630.
Therefore, 60% of Inga's monthly income is 0.6 * $6630 = $<<0.6*6630=3978>>3978. Answer: \boxed{3978}.