To solve this problem, we first need to convert all the mixed numbers into improper fractions.

2 2/9 = (2 9 + 2)/9 = 20/9
7 1/5 = (7 5 + 1)/5 = 36/5
11/12
7 1/5 = (7 5 + 1)/5 = 36/5
1 3/4 = (1 4 + 3)/4 = 7/4

Now we can plug these values into the equation:

(20/9) (36/5) + (11/12) (36/5) - (36/5) * (7/4)
= (720/45) + (396/60) - (252/20)
= 16 + 6.6 - 12.6
= 10

Therefore, 2 2/9 7 1/5 + 11/12 7 1/5 - 7 1/5 * 1 3/4 = 10.