A side can make only one move at the time, in this position black can jump either way, for example G7 x e5 and now it is white turn.
Which game are you designing? If this is English Draughts than they use a numerical notation and not a chess notation.
Is there a specific rule or regulation I can reference regarding this?
The only rule I can find is:
"If you are able to make a move that results in a capture then you must take it."
But this doesn't say anything regarding two different captures.
"If a player has the option to jump, he must take it." This makes it seem like both pieces must be taken.
And yes, it's English draughts.
1.20 All capturing moves are compulsory, whether offered actively or passively. If
there are two or more ways to jump, a player may select any one that they wish, not
necessarily that which gains the most pieces. Once started, a multiple jump must be
carried through to completion. A man can only be jumped once during a multiple
jumping sequence.
So in your diagrammed position Black has 3 choices of jump but can only select one of them.
7-16, or 8-15 or 9-18. In your notation E7 X G5 or G7 X E5 or B6 X D4.