How do I figure out if I can adjust the seat height on a kid's bike?

You can check if the seat is fixated onto a pole and has no extension. If it appears that it should be able to extend longer, than probably the screw is on too tight. You should ask the previous owner for some help. Good luck :)

The screw may just have frozen up if it hasn’t been used in a while. Get some liquid wrench or similar product and try that. Or if you are on good terms with your auto mechanic, take it to him and see if he will help you.

The picture looks like the white bit goes into the black. The screw thingy should turn. You may need some WD-40 or a pair of pliers to grip it if it is really tight.

The bike pictured definitely has an adjustable seat. Under the seat, where white starts is a bolt. I assume that’s the one you’re trying to turn. That’s the one that needs to turn but like has been mentioned, it’s probably just stuck. WD-40 is a good suggestion. Try it along with a wrench on the nut side and a screwdriver on the bolt side (if there is a slot for a screwdriver on the head of the bolt).

And remember, “righty, tighty; lefty, loosey”.

Thanks for the advice everyone. I assumed I could open it, but it was jammed really tightly. After a fair bit of coaxing with WD40 and some elbow grease, I managed to free the bolt and adjust the seat post.

Here’s a tip: pull the seatpost all the way out, wipe it with silicone grease, and reinsert it. The grease keeps the metal from seizing.

just be sure there is at least 2 inches of the seat post down inside the frame. If it needs to go higher than that you will need to get a taller seat post. That will also be a good sign that the bike is too small for the person so a longer seat post will mean you get some more time out of the bike before getting a bigger bike.