Elegant solution to a packing problem

I need to design a production line for soda cans and the last step is to put two 3x2 packs of cans, that are wrapped in plastic, on a cardboard tray thats already folded. The 2x3 packs come from a conveyor belt with the short side (2cans) parallel to the direction of travel. About a packet every 12 seconds. The trays can be supplied in any way (not manually), but preferably on a conveyor belt as well. The trays are made for 3\*4 cans (so 2 packs of 2\*3) and are about 5 cm tall (2 inch). My idea was to grab it from both sides with pneumatic cilinders and then move those over and down with other cilinders, but that would require double cilinders for the over movement since there's 2 different positions (front and back of tray) and it doesn't feel elegant or simple. I was hoping anyone could find an elegant solution for the problem. thanks in advance https://preview.redd.it/hbwm3dfnc87e1.png?width=642&format=png&auto=webp&s=d7be1b3f7c32947cc7c3c8549d0cb4f5ce151a16