Clearly 7 cannot be used.
To balance 3s, 3 & 6 must be on one side, 9 on on the other.
To balance 5s, 5 and 10 must be on opposite sides.
Once we have three numbers on one side, the fourth is obviously determined, so we have at most two possibilities:
3×6×5×8 = 9×10×2×4
3×6×10×4 = 9×5×2×8
Nice.