This instrument was an undistinguished "classical" style acoustic guitar. One obvious difference between a classical and a folk guitar is that classical guitar headstocks tend to have two parallel slots, and horizontal tuning pegs, with the knobs pointing to the back of the instrument, while a folk guitar has tuning pegs the poke up through a solid headstock. Classical guitars use nylon strings, while folk guitars usually have steel and/or bronze strings.

This guitar had the slotted headstock, but one set of tuning machines was installed upside down. Or backwards, depending on your point of view. One set of tuning pegs went back, the other projected toward the fretted side of the neck! And they didn't match. I assume that someone broke a peg and replaced the set, not realizing that the gear mechanism comes apart to reverse the orientation of the knobs.

But that's not why this guitar was in the trash. The bridge (where the strings attach to the body), had pulled completely off, and it was just dangling by the (steel) strings still attached to the headstock. Steel strings require higher tension when tuned, and so put more force on the bridge, and that's probably why it pulled off.

Gluing the bridge back on might seem like a trivial task, but the top of a guitar is thin and flexible, so it can radiate the sound. Thus, you can't just glue the pieces together and clamp them until it cures without pushing in the top. However, I have a small screw-jack (home-made) that I put inside the body to resist the clamping force. When the glue cured, I tied a new set of nylon strings onto it, tuned it up, and now my (adult) son is learning to play it. (Another difference between guitars is the width of the neck. This one is relatively wide, which is good, because my son has relatively fat fingers.)