It's a matter of proportion
This is a CG shift equation that you should commit to memory and become very comfortable working. Practice is the key.
Here we go:
Equation 1.: W / GW = CG Shift / Station Shift
That is: Amount of Weight to be moved is to the Gross Weight, as the Shift of CG is to Shift of Station.
Knowing any three of the variables will allow you to solve for the remaining unknown, viz.:
Equation 2.: W = (GW)(CG Shift) / Station Shift
Equation 3.: CG Shift = (W)(Station Shift) / GW
Equation 4.: Station Shift = (CG Shift)(GW) / W
In your specific problem, we are interested in the amount of Weight to be moved between two given stations so as to produce a given CG Shift; therefore, employ Equation 2. Substituting the given quantitities, this becomes:
W = (285,000)(2.3) / (1030 - 600)
Note that the term in the denominator is the difference, in inches, between the two stations given in the problem, and of course simplifies to 430.
Therefore the equation becomes:
W = (285,000)(2.3) / 430. Performing the math, W = 1524.4186 pounds (I will leave it to you to round this figure accordingly; by the laws of significant figures, it would be 1520 pounds; by ordinary rounding rules, it shoud be 1524 pounds; and as a practical matter, I would say 1525 pounds, since 1524 pounds would not be sufficient to move the CG a minimum of 2.3 inches; the latter consideration is probably splitting hairs, I grant you.)
You can either accept the explanation that the proportion given in Equation 1. is true, or go to any available study guide (ASA, Gleim, etc.) for an explanation as to how the formula is derived.
Good luck to you.