hey bob, sorry for the late reply man, i somehow missed your post
unfortunately, your right, 'nope, you got 120v'
the good news is that IF the plug in the shed is a 'home run' or dedicated line going from the panel, to the outlet in the shed, than making it 240v will be easy.
the not so good news is that if your 240v devices require a neutral (and alot of 240v lighting/climate controllers do) than you will have to run new wire.
if they dont, then this will be relatively easy.
pic one-
the good news is, if that spare breaker in the top right is not being used for anything, than you have the space and the equipment to do what you need to do to make the outlet in the shed 240v
the bad news is your lights in the shed are being fed from the 120v outlet... so your lights will have to go bye bye, or be replaced by fixtures that will run off of 240v. and i dont mean the grow lights, i see a switch next to the outlet in the shed, and im assuming that switch feeds a light somewhere inside or outside the shed...
pic two- it appears that the circuits in question are sharing a two pole breaker, instead of two seperate single pole breakers as they should be
pic three- yep, thats a light switch being fed from the same circuit as the receptacle, as mentioned above.
pic four- that looks like a 120v 15amp GFCI outlet... could be a 20 though. but its 120v, no doubt about it.
in the shed-
the ideal thing to do would be to get rid off whatever lights are currently being fed from that switch.
get rid of that gfci and put in a 3 prong 240v outlet.
and then, in the main panel
remove the spare wire going to the attic from the 15 amp breaker on the top right.
remove the wire from the breaker feeding the garage (circuit 12)and move it to the breaker in the top right.
remove the neutral (white wire) from the neutral bus that is for the shed (circuit 14)
connect the neutral to the other pole of the 20 amp 240v breaker (circuit 12)
and that should give you 240v in the shed...
this is something you should only do if you are certain that the wire going to the shed is not sharing a neutral with another circuit. (like the one in the garage) this means that there must be a dedicated cable running from the outlet in the shed directly to the panel, and not connected to anything else in between... there is a way to test that but the test should only be performed by a qualified electrician, as there is significant risk of electrocution in performing the test. however, if you can see the cable with your eyes running to the shed, and your positive that its a dedicated line, then I could do the procedure i just explained as fast as 15 mins, and thats being ultra conservative in my time estimate.
as far as running a new cable, with a new breaker, its hard for me to estimate what it would cost, theres alot of factors to consider, how far is the run, does it have to be concealed, does it have to be buried, does it have to be in conduit or can it be direct burial cable, does your service have enough available ampacity, etc etc theres hundreds of variations that effect pricing.