To solve the given equation, first distribute the terms on both sides:

3(x-2.1) - 2(x-3.2) = 4x - 0.5
3x - 6.3 - 2x + 6.4 = 4x - 0.5

Combine like terms:

x + 0.1 = 4x - 0.5

Now, isolate x by getting all the x terms on one side of the equation:

0.1 + 0.5 = 4x - x
0.6 = 3x

Finally, solve for x:

x = 0.6/3
x = 0.2

Therefore, the solution to the equation is x = 0.2.