Can I convert 2 two-pole 60A breakers into 3 two-pole 40A breakers
Well designed, mostly.
So what we're looking at here is a commercial 120A tankless heater with its cover removed, and next to it, a Siemens 4-space subpanel.  All in a custom equipment bay that's been drywalled.  I'd guess a cabinet door swings over this? Well done.
The good news is, &quot;the last guy&quot; really did this right in the large sense, bringing a single 125A feeder from your main panel to this subpanel.   It only takes 2 breaker spaces in your main panel, and it means you can fit any of  the 120A-class water heaters here, whether they take 2, 3 or 4 circuits to power them.
The bad news is, &quot;the last guy&quot; in the small sense did did exactly the thing we constantly warn people about: using a subpanel that is barely enough for immediate needs and provides no room for future expansion.  Now, since the water heater accounts for 96% of the panel's capacity, there isn't really any room to hold anything else, but gosh, the price difference to a 6-space panel wasn't even a latté and would have protected the case of a 3-circuit water heater, as many are made.
But it's still good.
While this usually doesn't work anymore, in this particular case we can fall back on the trick of using &quot;double-stuff&quot; breakers.  This panel is a dead-ringer for a Siemens/Murray E0408xx1125 panel, so assuming it's a Siemens...
Siemens does indeed make a breaker that crams two 40A/240V breakers into 2 spaces, the Q24040CT2.  And indeed, the outer poles have common trip.

This bad-boy goes in one of the double breakers spaces.  A run-of-the-mill Siemens 40A breaker ($10) goes in the other. You now have three 40A circuits.
Remember, just as the handle-ties suggests, one of the circuits goes on the inner screws, and the other circuit goes in the outer.  Very important!
You need to mark the wires! (the last guy didn't)
Wire needs to be #8 copper or larger.  #6 aluminum will also work.  White wires need to be re-marked with tape because they'll be used as hot wires. Black will do, but for style points --
-- actually, hold on.  There isn't really a need or purpose to distinguish the two hot wires from each other.  However it is absolutely vital to distinguish them by circuit.  So I recommend re-coloring both black and whites in each cable, making the same color in each cable.   E.G.

Cable 1 becomes yellow, yellow, ground*
Cable 2 becomes blue, blue, ground
Cable 3 becomes red, red, ground.

They sell a 5-pack of colored electrical tape for like $4. This will assure a &quot;pro looking&quot; installation, and make it very easy for you to keep the circuits straight.

* Black-black-ground is also fine here, but I figure if you don't own any black electrical tape, you can get by with just the 5-color pack :)