To solve this equation, we first need to convert 1 4/3 to an improper fraction.

1 4/3 = (3*1 + 4) / 3 = 7/3

Now, we can rewrite the equation:

7/3 ÷ 7 = 0.2x ÷ 3

Next, we simplify the left side of the equation:

7 ÷ 7 = 1

So, the equation becomes:

1 = 0.2x ÷ 3

To solve for x, we multiply both sides by 3:

3 = 0.2x

Divide by 0.2 on both sides:

x = 3 / 0.2
x = 15

Therefore, the solution to the equation 1 4/3 ÷ 2 1/3 = 0.2x ÷ 3 is x = 15.