Press your lips together. Air flows through your nose. Vocal cords vibrate.

Americans pronounce mule as MYOOL (/mjul/). The L in "mule" 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 MYOOL. You'll hear it in sentences like "The mule refused to move for the huge cute".
Record yourself saying "mule" 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.
Press your lips together. Air flows through your nose. Vocal cords vibrate.

Start with the tongue mid-front raised high, almost touching the roof of the mouth (but not touching). Glide into a tight lip circle as the tongue back lifts.
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 "mule" 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.