Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Americans pronounce wheel as WEEL (/wil/). The L in "wheel" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. This is called the Dark L vs Light L, and it's why Americans sound more relaxed than the textbook. It comes out as WEEL. You'll hear it in sentences like "I took a pottery class to learn how to use the throwing wheel".
Record yourself saying "wheel" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 3 sounds. Explore each sound's mouth shape and how it's made.
Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Pull the corners of your lips back slightly. Arch the middle-front of your tongue high toward the roof of the mouth.

Keep the tongue tip down and pull the back of the tongue up toward the throat. The 'dark' sound comes from the back.

The textbook way isn't wrong — it's just not how anyone actually says it.
The L in "wheel" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. Dark L adds a small schwa-like "uh" before the L. The back of the tongue lifts toward the soft palate.