Ah yes, reroll aces is NOT reroll 1s, as you may expect. It's actually an exploding dice mechanic.
You can just remove the second number in the square brackets in the result and use the 6 that was initially rolled. With that, I make you having:
4d6 - ( 1, 1, 1, 3 ) = 6 - 1 = 5
4d6 - ( 1, 3, 2, [ 6, 3 ] ) = 15 - 3 - 1 = 11
4d6 - ( 2, 1, 5, [ 6, 4 ] ) = 18 - 4 - 1 = 13
4d6 - ( 4, 2, 1, 3 ) = 10 - 1 = 9
4d6 - ( 5, [ 6, 2 ], 5, 2 ) = 20 - 2 - 2 = 16
4d6 - ( [ 6, 4 ], 4, 1, 1 ) = 16 - 4 - 1 = 11
16, 13, 11, 11, 9, 5
If you don't like that array, feel free to try a "clean" roll of 4d6s and go from there.