I get confused on how to do the signs
You want to isolate y on one side, and the rest on the other.
Start by adding 7y to both sides to get 6 + 4x/3 = 1 + 7y
Then subtract 1 from both sides to get 4x/3 + 5 = 7
Now, divide both sides by 7. (4x/3)/(7) + (5)/(7) = y
Simplifying, we get 4x/21 + 5/7 = y
Wait... doesn't y belong on the left? We usually see it that way, but the Symmetric Property of Equality says that if a = b then b = a. Therefore, we can rewrite the equation as y = 4x/21 + 5/7