First, let's simplify the expression on the left side of the equation:
(4 10/27 + x) - 8 4/27

Convert 4 10/27 to an improper fraction:
4 10/27 = (4*27 + 10)/27 = 118/27

Now, substitute this back into the expression:
(118/27 + x) - 8 4/27
= (118/27 + x) - (8*27 + 4)/27
= (118/27 + x) - 220/27
= (118 + 27x - 220) / 27
= (27x - 102) / 27

Now, set this equal to 22 1/27 and solve for x:
(27x - 102) / 27 = 22 1/27
27x - 102 = 27(22) + 1
27x - 102 = 594 + 1
27x = 696
x = 696/27
x = 259/27

Therefore, x = 259/27 or approximately 9.59.