What would be the score count for a hand with 3 - fours and 1 - seven my thought is 12. For 3 - fours equal 6 points (3 royal pairs) and the three royal pairs of 2-fours and the seven = 6 points.
If I read you correctly, you're describing a hand like 4H 4D 4S 7D.
- 4H 4D 7D - 15 2
- 4H 4S 7D - 15 4
- 4D 4S 7D - 15 6
- 4H 4D - pair (2 points)
- 4H 4S - pair (2 points)
- 4D 4S - pair (2 points)
You are indeed correct that this adds to 12 points. You are also correct that you can shortcut the pairs to 6 points as Pair Royal.