Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

Americans pronounce inquiry as ihn-KWAHY-ree (/ɪnˈkwaɪri/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "Thank you for your prompt response to my inquiry".
Record yourself saying "inquiry" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 7 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

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

Start with your jaw open wide and your tongue resting low and flat. Glide the front of your tongue up toward the roof of your mouth as your jaw closes halfway.
The textbook way isn't wrong — it's just not how anyone actually says it.
Stress falls on the second syllable, not the others. Stretch KWAHY — keep everything else short and quick.