Expanding both sides of the equation we get:

4(0.7x) - 4(4) - 3(-0.2x) + 3(6) = 0
2.8x - 16 + 0.6x + 18 = 0

Combining like terms we get:

3.4x + 2 = 0

Now, isolate the variable by subtracting 2 from both sides:

3.4x = -2

Finally, divide by 3.4 to solve for x:

x = -2/3.4
x = -0.5882 (rounded to 4 decimal places)

Therefore, the solution to the equation 4(0.7x-4)-3(-0.2x+6)=0 is x = -0.5882.