To solve this equation, we first need to combine like terms on both sides and then simplify.

Starting with the left side of the equation:

$2x-3$/12 - $5x-11$/2
= $2x-3$/12 - 6$5x-11$/12
= $2x-3-30x+66$ / 12
= $-28x+63$ / 12
= -28x/12 + 63/12
= -7x/3 + 21/4

Now, simplifying the right side of the equation:

$x+3$/6 - $x+2$/3
= 2$x+3$/12 - 4$x+2$/12
= $2x+6-4x-8$ / 12
= $-2x-2$ / 12
= -2$x+1$ / 12
= -2x/12 - 2/12
= -x/6 - 1/6

Now we set the two sides equal to each other and solve for x:

-7x/3 + 21/4 = -x/6 - 1/6

First, let's get rid of the fractions by multiplying everything by 12:

-28x + 63 = -2x - 2

Now, add 2x to both sides and subtract 63 from both sides:

-26x = -65
x = -65 / -26
x = 5/2

Therefore, the solution to the equation is x = 5/2 or x = 2.5.