To solve this equation, we first need to simplify both sides:

4/7 * (1/2 - x) = 4/3 + 0.2

Multiplying 4/7 by 1/2 gives us 4/14 or 2/7:

2/7 - 4/7x = 4/3 + 0.2

Next, we can combine the constants on the right side:

2/7 - 4/7x = 14/10 + 2/10

2/7 - 4/7x = 16/10

Now, we can multiply both sides by 7 to get rid of the denominator:

2 - 4x = 112/10

2 - 4x = 11.2

Subtract 2 from both sides:

-4x = 9.2

Divide by -4 to solve for x:

x = -9.2 / 4

x = -2.3

Therefore, the solution to the equation is x = -2.3.