I have a hot and cold hose bib in the garage for washing dogs, car in the winter, muddy hunting gear etc. It quit letting the hot water through.

It's vertical valves with a blend chamber cast into the body, single outlet on the bottom.

I shut off the water, pulled the hot valve bonnet and stem. Can't see anything up inside but a flat shiny piece.

What would cause this? How hard is it to replace the whole thing? I'm sure it's on pex, but don't know if there's enough slack to pull it out.

Turn water on without bonnet to see if anything came out?

I tried that too. Thought if there was an obstruction it might clear it. Not even a drip came out.

Is there a shutoff valve somewhere in the line that could have got plugged or turned off?

I don't think so, the same water line feeds the washer just a few feet inside on the same wall.

It's one of these i think.
https://www.prier.com/products/c-108/

Hire a local reputable plumber to either fix or replace.

Before delving into the world of plumbing make sure you memorize the Plumber’s Creed:

“Hot on the left, cold on the right, chit flows downhill so put a slope on the pipe, payday’s Friday and the boss is a SOB.”

Welcome Union Brother.

And

Don’t chew your fingernails.

That link says it has internal checks.
Can you open it up and see if it has failed?

Checks keep hot from miigrating to cold line and vise versa

You left out one of the most important rules......I fixed it for you.....

Item #14 on the parts list, 'back flow check valve' ain't opening anymore.

That's the hard part. Reputable in a good way seems hard and expensive to find. There's been enough new growth around here to attract lots of worthless schiesters.

So part# 14 is directly attached to the stem, is soft rubber, like a cup. I removed the entire stem and turned the water on. Nothing came out.

Don't lick your lips either.

Y’all are plumber literate. I worked a while in a small pipe fabrication shop on a steam plant site back in the mid 70s. Pipe fitters are a world unto themselves especially travelers after overtime. I had the dubious honor of handling time and paycheck delivery for the guys out of our shop. Hard times in a way but thankful for the experience. A man needs to have varied exposure to how others live and work. Still have some of the spool sheets I did and handed off to the fabricators. Graph paper drawings that are less than archaic compared to computer generated today but i like knowing they were accurate and to the best of my ability. Computer generated don’t show the day to day interactions of field drawing to installed spool and the guys that did it all. Anyhow.

Try to get a mfg. name and model number. Google it. Much info is available online. Sounds like it is a mixing valve and probably has an internal spool piece(like a piston) that is stuck. Take it apart, clean it up, put plumbers grease on it and reassemble it. Give it a try. Worst that can happen is you will need to call a plumber if you screw it up.

So your problem is likely with your hot water supply not your mixer.

Did the seat washer seperate?
There is a small brass screw #4 on diagrahm,that holds a washer in place Alot of the washers will break down over time ,mostly on the hot water side.
Check that there is good hot water at the washer as well.

He should've had a flood when he pulled the stem and turned on the water.

Maybe let a 22 short rip down through there and see if it opens it up.