how do I do this

Solve for x. 3x – 2y = 6

Add 2y to both sides and then divide both sides by 3, to give you just "x' on the left side.

so is this how i work it out
3x-2y=6
3x- 2y= 6 -2y
3x=6-2y
x= 2 +2y

No.
Add 2y to both sides.
3x- 2y+2y= 6 +2y
3x=6+2y
divide both sides by three.
3x/3 = 6/3 +2y/3
x=2+ 2/3 y
You made a lot of errors adding and dividing.

No. You did not add 2y to both sides-- you subtracted. Your subsequent algebraic manipulations are also all wrong. Here is what you should have done.
3x - 2y = 6
3x = 6 + 2y
x = 2 + 2y/3

It appears to me that you would benefit from a tutor. Discuss this with your mom. Probably another student in your class...your teacher can suggest one. You seem to be trying, but are missing a lot of details.

graph 3x+2y=6

To graph the equation 3x + 2y = 6, you can follow these steps:

1. Rewrite the equation in slope-intercept form (y = mx + b) by isolating y:
2y = -3x + 6
y = (-3/2)x + 3

2. Determine two points on the line. To do this, choose any x-values and plug them into the equation to solve for y. Let's choose x = 0 and x = 3:
For x = 0:
y = (-3/2)(0) + 3
y = 3
So one point is (0, 3).

For x = 3:
y = (-3/2)(3) + 3
y = -9/2 + 6/2
y = -3/2
So another point is (3, -3/2).

3. Plot the two points on a coordinate plane.

4. Draw a straight line passing through the two points. This line represents the graph of the equation.

Here's a visualization of the graph:
![Graph](https://www.wolframalpha.com/Calculate/MSP/MSP69731i29f501465hi6c0000670g6c1gc3a2i386?MSPStoreType=image/gif&s=28)

You can see that the line intersects the y-axis at the point (0, 3) and has a negative slope (-3/2).