To subtract the second mixed number from the first mixed number, we need to first convert both mixed numbers to improper fractions.

10 9/16 = (16*10 + 9) / 16 = 169/16

3 11/12 = (12*3 + 11) / 12 = 47/12

4 4/9 = (9*4 + 4) / 9 = 40/9

Now, we can subtract the sum of the second mixed numbers from the first:

169/16 - (47/12 + 40/9)

First, find a common denominator for the fractions within the parentheses:

12 and 9 have a common multiple of 36.

Rewrite 47/12 and 40/9 with a denominator of 36:

47/12 = (47/12) * (3/3) = 141/36

40/9 = (40/9) * (4/4) = 160/36

Now we can perform the subtraction:

169/16 - (141/36 + 160/36)
= 169/16 - 301/36
= (1699)/(169) - (301/36)
= 1521/144 - 301/36
= (1521 - 432) / 144
= 1089/144
= 27/4

Therefore, 10 9/16 - (3 11/12 + 4 4/9) = 27/4 or 6 3/4.