To estimate a fraction (I'll use 9/52 for an example), you have options:
A) You could round the denominator to a round number, such that (1/that denominator) is an easily recognized decimal. So 9/52 would round to 9/50, and since 1/50 = 0.02, 9/50 = 0.18.
B) You could round the denominator to a multiple of the numerator, so that you can reduce both top and bottom to something recognizable. So 9/52 would round to 9/54 = 1/6, which you should memorize as 16.6% (or you should quickly recall that 1/6 is half of 1/3 or half of 33.3%).
How you can Estimate 11/30 of 6/20 of 120
I did not understood the method shown in Manhattan guide
In your example, there are two fractions. Before rounding either one or both of them, first see whether you can cancel between them:
11/30 * 6/20 (6 is a factor of both 6 and 30, so cancel that!)
=11/5 * 1/20
In this particular case, I think no fraction estimation is really necessary, since 100 is such a nice denominator.
11/100 = 0.11
Maybe the estimation comes in at the calculation of 11/100 of 120. Since 0.11 is a little more than 1/10, the answer will be a little more than 1/10 of 120, or a little more than 12.