So I see you are on the right track elsewhere. I personally dislike how division is taught and even notated in most early math classes. I am going to rewrite your problem in a way that makes it much clearer (for me) and hope it helps you.
Division is the inverse of multiplication. Taking something divided by two, is the same as multiplying something by one half. If you can agree with that: X/2 = 0.5 * X, then we are on our way.
Your problem can be thought of like this:
(2X+3)(1/4) - (3X-5)(1/3) = 2
You find your least common multiple to get rid of those fractions. In this case 12.
Whenever you do anything to one side of an equals sign you have to do it to the other side.
Further, multiplication is commutative, so it has to apply to everything on both sides.
In this case:
12[(2X+3)(1/4) - (3X-5)(1/3)] = 12[2]
You can simplify here. The right side is easy. 12* 2 =24. The left side is a little busy. Whenever you have a math "sentence" you can think of addition and subtraction as spaces between "words".
You have to multiply 12 by the whole "sentence". This sentence is composes of 2 "words". Each of those "words" must be multiplied by 12.
In this case: 12[(2X+3)(1/4)] and 12[(3X-5)(1/3)]
This is still maybe a little busy. But remember it doesn't matter what order you multiply things in. 234 = 423.
In this case: 12(1/4)(2X+3) can turn into 3(2X+3). We took the 12 and the 1/4 and combined them into one term. 12(1/4) is the same as 12/4, which is 3.
Like earlier, this 3 multiplying the parentheses has to be applied to both "words" in that section.
In this case: 32X + 33 simplifies to 6X + 9.
Now the other term: 12(1/3)(3X-5)
12 * 1/3 is 4.
Therefore: 4*(3X-5)
43X - 45 is 12X-20
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So putting it all back together:
(6X+9) - (12X-20) = 24
Now we get rid of the parentheses.
6X+9-12X+20 = 24
Why did the 20 become a plus? Because subtraction can be thought of as adding something times (- 1) and when you multiply something it applies to all the words in the sentence. So (6X+9) + (-1)*(12X-20)=24 is a different way to look at that equation. Multiplying the negative one to both "words" in the "sentence" is it affecting would make them into - 12X and - - 20. - - is the same as +. So +20.
Finally we combine things:
6X-12X+20+9 = 24 -6X+29=24
then we move the 24 over by removing 24 from both sides -6X+29-24=24-24 -6X+5=0
Then we move the 6X over by adding 6X to both sides. -6X+6X+5=0+6X 5=6X
Finally we get X alone by diving both sides by 6. 5/6 = 6X/6 5/6 = X
Hopefully this helps you.
If you have questions I can try break it down further. Otherwise YouTube is a fantastic tool if you benefit from a visual walkthrough. I would start by looking up Algebraic Fractions or Algebra woth Fractions and see if any thumbnails look like your problem.
Good luck!