Without going into details, I say, no you are not right. Because how can 120/6600 be greater than 1?
Or did you mean, 6600/120? That, sure, is 55.
Now let us see the fractions.
(4 1/6)*(4 4/5)*(2 3/4)
The usual way is to change the improper fractions into proper fractions, then multiply all the numerators, same with all the denominators.
So,
= ((6*4 +1)/6)*((5*4 +4)/5)*((4*2 +3)/4)
= (25/6)*(24/5)*(11/4)
= (25*24*11)/(6*5*4)
= 6600/120
Hey, you are right!