Show canned hints
Each color of each gate has a different transformation. Play around with them until you find some that make it easier to understand what the inputs are.
Try making the bowtie gates red, the pentagon gates blue, the pawn gates red, and the two-input gates blue. Do you notice anything about the outputs?
The first few inputs, to help you figure out the gates, are: SWING, PELOSI, BOAST, HAM, PROMO, EAVES.
|xor, and, or||
The symbols for the two-input gates will help you figure out the functions for their red meanings.
The color of the lines between the nodes - pink or black - refers to whether the value traveling along that line is a word or not.
the AND gate is the hardest to figure out. Blue is overlapping letters, e.g., REMOTE and DENOTE make EOTE. Green is a caesar shift of the second word by the first letter of the first word.
Once you've gotten most or all of the right intermediate outputs, apply the functions you've learned to figure out what the overall output of the circuit is.