To solve this equation, we first need to find a common denominator for the fractions on both sides of the equation. In this case, the common denominator is 24 (since 6 and 8 both divide evenly into 24).

Rewriting the equation with a common denominator, we get:

(4(3x-1) - 3(2x+3))/24 = 2

Expanding the terms inside the parentheses, we get:

(12x - 4 - 6x - 9)/24 = 2

Combining like terms, we get:

(6x - 13)/24 = 2

Multiplying both sides by 24 to get rid of the fraction, we get:

6x - 13 = 48

Adding 13 to both sides, we get:

6x = 61

Dividing by 6, we get our final solution:

x = 61/6 = 10.1667 (rounded to four decimal places)