To solve this equation, we will first simplify the expression on the left side of the equation:

1/5у - (6 - 4 2/3) = 8 1/3
1/5у - (6 - 14/3) = 25/3
1/5у - (18/3 - 14/3) = 25/3
1/5у - 4/3 = 25/3

Next, we will get rid of the fraction on the left side of the equation by multiplying both sides by 15 (the least common multiple of 5 and 3):

15(1/5у - 4/3) = 15(25/3)
3y - 20 = 125

Now, we can isolate the variable y by adding 20 to both sides:

3y - 20 + 20 = 125 + 20
3y = 145

Lastly, divide both sides by 3 to solve for y:

3y/3 = 145/3
y = 145/3

Therefore, the solution to the equation is y = 145/3.