To solve this equation, we first want to simplify the left side by combining like terms.

Starting with the variable terms on the left side:
4b - 2b = 2b

Now we have:
2 - 2b = 1/6 + 3b

Next, we want to isolate the variable term on one side of the equation. Let's start by moving the 1/6 term to the left side by subtracting it from both sides:

2 - 2b - 1/6 = 3b

To simplify, we find a common denominator for 2 and 1/6, which is 6:
(12/6) - (2b + 1/6) = 3b
(12 - 2b - 1)/6 = 3b
(11 - 2b)/6 = 3b

Now, we can multiply through by 6 to get rid of the denominator:
11 - 2b = 18b

Next, we want to combine like terms on the left side:
11 = 20b

Finally, to isolate the variable "b", we divide by 20 on both sides:
b = 11/20

Therefore, the solution to the equation 4,2-0,2:(1/6+3b)=3 3/5 is b = 11/20.