This is the Bode plot of a Broadband Bandreject Op Amp amplifier. The exercise says this:

I know that in order to get both cutoff frequencies I need to subtract 3 dB from the plot, but how do I get the gain? I would think that the gain is 3 dB because it is also the distance between the top of the graph and the cutoff frequencies, but wouldn't that imply that the gain would ALWAYS be 3?

It's a gain of 3 not a gain of 3 dB! They just say that you have about 9.5dB on the left and the right so the signal is multiplied approximately by a factor of 3.

You want to look at the pass band gain, just read off the graph. Look at the graph at the low frequency and high frequency where the plot level off at about +9dB. Gain in dB is 20 log G, where G is linear gain. So +9dB give G≈2.81. But I just roughly read +9dB, so it is likely gain of 3, I like to stay with simple number of +9dB rather +9.54dB or something.

The notch filter is the -3dB on each side, so if you consider pass band gain is +9dB, then look at the two points of the graph crossing +9dB-3dB=+6dB.