First, let's convert all mixed numbers to improper fractions for easier calculations:

-6 2/3 = -20/3
2 3/4 = 11/4
-3 1/6 = -19/6
9 -11/21 = 189/21 - 11/21 = 178/21
-2/3 -3 = -2/3 - 9/3 = -11/3

Now, let's add and subtract:

-20/3 + 11/4 - 19/6 + 178/21 - 11/3
= (-140/21 + 231/21 - 70/21 + 178/21 - 77/21)
= 222/21
= 74

Next, let's calculate the decimal subtraction:

-3.17 - 2.7 = -5.87

Therefore, the final answers are:
-20/3 + 11/4 - 19/6 + 178/21 - 11/3 = 74
-3.17 - 2.7 = -5.87