The big track look is 13 hexes, so arm 1 needs to travel it 6 times to get back to its starting rotation. At this rotation, it can grab a reagent at the first bottom point of the track, and transfer a reagent from the bottom middle to arm 6. 
However, it cannot do both of these in sequence, because the reagent is stored off to the left until arm 1 passes the second bottom point. Because of this, arm 1 takes 6 track loops to grab a reagent, and another 6 to send it to the second chamber. 
In the second chamber, arm 8 will grab 1/5 of these reagents to turn them into products, while the remaining 4/5ths get trashed