Hi Ron, welcome to AGO on-line! Also, thank you for your service!
That looks like a pretty deep scratch.. One thing when compounding a car is to have uniformity in appearance. Meaning, you don't want to just compound the scratch, you want to do the whole car for uniformity.
The best approach is to make sure you do proper surface prep, wash, iron-x decon, wash again, and clay. This will remove all the contaminants on the paint which will give a better surface for the compounds to work.
Secondly, you're going to want to apply the least aggressive approach. Meaning, you may want to start with a polishing pad and a lighter cut polish. Do your section passes and see how the paint looks. If it clears things up, you may be fine to do the rest of the car. If you need to move up, move up in the cut of the pad vs. product. then increase the cut of the product.
This is why most vendors make products in stepped cut... i.e.
Pinnacle Advanced Finishing Polish - a fine cut polish
Pinnacle Advanced Swirl Remover - a medium grade compound
Pinnacle Advanced Compound - a heavy cut DAT compound.
Or GG
BOSS Fast Correcting Cream
BOSS Correcting Cream
BOSS Finishing Polish
See a pattern here??? You may need more than one system... If your cut is too strong, you may need to go over it with a polish to remove marring caused by the heavier cut compound.
And at the end of the day, if you used the most aggressive method, and the scratch is still there, be prepared to accept it and walk away. Any attempts at further correction may lead to burning through the clear-coat (heat of the pad / machine must be taken into consideration). Be satisfied with about 70% correction.
