The first portion of your work is correct. The graphs of the two equations intersect at x=-3 and x=2. However, there is a discrepancy with the y-coordinates of the intersections. Let's go over it to clarify.

The given equations are:

`y=x^2`

`y= 6-x`

To solve for their intersections, set the two y's equal to each other.

`y = y`

`x^2=6-x`

`x^2+x-6=0`

`(x+3)(x-2)=0`

`x+3=0` `x-2=0`

`x=-3` `x=2`

Then, plug-in the x values to either of the original equations. Let's use the second equation y=6-x.

So, when x=-3, the y value is:

`y=6-(-3)=9`

And, when x=2, the y value is:

`y= 6-2=4`

Hence, the points of intersection are (-3,9) and (2,4).

Next, to get the distance between these two points, apply the formula:

`d = sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

`d=sqrt((2-(-3))^2+(4-9)^2)`

`d=sqrt(5^2+(-5)^2)`

`d=sqrt50`

`d=5sqrt2`

**Therefore, the distance between the points of intersection of the graphs of the two given equations is `5sqrt2` units.**