To simplify this expression, we need to first work within the parentheses, then combine like terms.

(2 7/27 + 3 4/21)
Convert the fractions to have a common denominator of 27:
2 21/27 + 3 36/27
Now add:
5 57/27
Reduce the fraction:
5 19/9

(9 2/21 - 8 4/21)
Convert the fractions to have a common denominator of 21:
9 2/21 - 8 4/21
9 2/21 - 8 12/21
Now subtract:
1 - 4/21
Convert fraction to have a common denominator:
1 - 1/21
20/21

Now we have:
7 5/21 - (5 19/9) - (1 20/21) + 4 6/21

Subtract the fractions within the parentheses:
5 19/9 - 1 20/21
Convert fractions to have a common denominator of 63:
5 209/63 - 1 60/63
Now subtract:
4 149/63

Plugging back into the original expression:
7 5/21 - 4 149/63 + 4 6/21

Add or subtract whole numbers and fractions separately:
7 - 4 + 4 = 7
5/21 - 149/63 + 6/21
Convert fractions to have a common denominator of 63:
15/63 - 149/63 + 18/63
Now subtract:
15 - 149 + 18 = -116
So, the final simplified expression is:
7 - 116/63