To solve this equation, we will first simplify both sides of the equation:

7$х-6$/4 = 5$х+1$/3 - 3$х+2$

To simplify the left side, distribute the 7:
$7х-42$/4 = 5$х+1$/3 - 3$х+2$

Next, simplify the right side by distributing the 5 and 3:
$7х-42$/4 = $5х+5$/3 - $3х+6$

Now, find a common denominator for the fractions on the right side, which is 12:
$7х-42$/4 = $4(5х+5)$/12 - $3(3х+6)$/12

Simplify the fractions on the right side:
$7х-42$/4 = $20х+20$/12 - $9х+18$/12

Combine the fractions on the right side:
$7х-42$/4 = $20х+9х+20-18$/12
$7х-42$/4 = $29х+2$/12

Now, clear the fractions by multiplying by 12:
12$7х-42$/4 = 12$29х+2$/12
3$7х-42$ = 29х + 2

Distribute on the left side:
21x - 126 = 29x + 2

Subtract 21x from both sides:
-126 = 8x + 2

Subtract 2 from both sides:
-128 = 8x

Divide by 8 on both sides:
x = -16

Therefore, the solution to the equation 7$х-6$/4 = 5$х+1$/3 - 3$х+2$ is x = -16.