Just want to make sure since I don’t feel like being electrocuted. I have a three wire running from the panel to the brewcommander. Using the neutral wire for the second hot. Does the picture look correct?
Looks good, the black and white wires will be your 2 hot legs and the bare wire goes to ground.
I believe code requires the white wire to be wrapped in red or black tape or colored with a marker so that it doesn't get confused as a neutral wire. Since you'll probably be the only one messing with it it's not really necessary.
It wouldn't hurt to double check in the main panel to confirm that the 3 wire cable's red and black wires are on the dryer breaker and the white is connected to the neutral buss.
There are 4 wires from the dryer plugin- red,black,white,green. I was just confused since I'm going from 4 wires to three so I want to make sure that the GFCI will trip. I would assume the test button will tell me if it's correct though?
You're fine going from 4 to 3 since your controller doesn't require a neutral wire. If you had an old house that only had 2 wires and a ground to your dryer you would have to put the GFI breaker in at the panel so that you could hook up to the neutral buss