Adding 50 amp breaker to 90 amp subpanel
Your panel has many &quot;tandem&quot; breakers... read here on what those are, how those work and  how they relate to panel spaces.
First, deal with  the fire-starters!
OK, there are at least three Multi-Wire Branch Circuits in here that are catastrophically miswired. They will overload neutral, putting  30A on a 15A wire.  &quot;The last guy&quot; did exactly the thing we warn people not to do: put MWBCs on tandems.
What's more, the installer violated the &quot;handle-tie&quot; rule of MWBCs, which would have prevented the blunder.

You will need two of (in order of preference) Eaton BQ215215, or BQC215215. Either one will do. You need two.
Pull the 8 wires off the bottom 4 left-side breakers.
Now, identify the three cables coming in that have  black-white-red.
Pick one cable.  Follow its black and red wires.  Stick them on the inner terminals of one of the breakers.
For the second cable, stick its black and red on the outer terminals of that same breaker.
For the third cable, stick its black and red on the inner terminals of the other breaker.
The two single-pole 15A circuits that are now dangling, go on the remaining breaker terminals.
Remove the bottom 4 breakers altogether, and snap these two quadplex in their place.
OK, so that's fixed. They have mandatory handle-ties, and they are correctly phased so you won't get a neutral fire.
Install the 50A breaker.
Now, get a BQC2502120, or a BQC220250, in order of preference.   This has 50A in the middle and 20A outside.
Remove the 20A single breaker.  Replace it with the above breaker.
Put the existing 20A wire on the bottom terminal of the big BQC breaker.
Put the 50A load on the middle terminals.
Now you have 1 spare 20A breaker, and one full slot still free.
Plan on replacing that panel with something much bigger soon.  As expected, you ran out of spaces before you ran out of amps.
Fix the markings on that panel.
They are a code violation for two reasons: First they specify rooms by things only you know like Karen's room, and second, they contradict each other.
Obviously someone rearranged this panel, and that's how the MWBCs got dangerously placed on tandems.
Also you are required to identify breakers by marking that will be obvious after you move out -- &quot;northwest bedroom&quot; not &quot;playroom&quot; and definitely not &quot;child's name&quot;.
Just get some acetone or something and wipe off all that Sharpie (not that easy)... better yet, scrub it with a Scotchbrite pad (so the paint will stick), clean and dry it, then hit it with a can of Krylon. Great time to match it (roughly) to your walls - you are better off using an &quot;oil paint&quot; like is in spray cans, than a latex which doesn't work on machinery.
Number all the spaces the same way -- 1A-1B through 12A-12B is fine, or 1-24, whatever. If an AFCI breaker is sitting on 23 and 24, people will figure out what you mean when you say &quot;23 NW Bedroom&quot; or whatever.