There isn't a lot I can tell you that you probably don't already know, but I'll try.
Pvt. Carter entered service from Oklahoma, and was KIA, 7 Jul 44, during the Normandy Campaign.
His unit was one of three Infantry Regiments (357th, 358th, 359th)in the 90th Infantry Division;
the 357th was assigned to 4th ID, and assaulted Utah Beach, Normandy, France, 6 June 1944, D-Day;
the remainder of the division attacked 10 Jun 44;
it was assigned to VIII Corps in this period.
Stanton states "Advancing in heavy rain, the division attacked 3 Jul 44, south down the west coast of the Contenin Peninsula, and fought the Battle of La Haye-du-Puits-Mont Castre Forest, 6-10 Jul 44."
William most likely fell victim during this engagement.
Another reference states:
6 July 1944, France; The American VII and VIII Corps continue their their slow advance to the south in the directin of Lessay and Periers against exceptionally fierce German resistance.
7 July 44; In the west the 79th ID and 90th ID (VIII Corps)continue their efforts to break through the defensive line between La Hay-du-Puits and Mont-Castre-Forest, but have to withstand violent counter-attacks.
8 July 44; VIII Corps overrun LaHay-du-Puits.
9 July 44: VIII Corps, trying to push beyond La Hay-du-Puits, is pinned down by the terrain and by te stiff resistance of the divisions of the German LXXXIV Corps.
10 July 44: In the VIII Corps sector the troops advance south of La Hay-du-Puits."
That is about all that I can come up with at the moment.
I hope that this helps youin filling out a profile on your dad.
I am sad to report that he was 1 of 3,342 men from the 90th ID who died in the 308 days it was in combat.