Place the very tip of your tongue slightly between your teeth. Blow air gently around it without voicing.

Americans pronounce thank as THANGK (/θæŋk/). In "thank", the "a" vowel before NG shifts toward "ay" — sounding like "ay" as in "say", a distinctly American pattern — most prominent in Midwestern American English; other GenAm speakers may use a less raised vowel. This is called the Cat-Vowel Before NG, the kind of sound shift that makes everyday speech feel effortless. It comes out as THANGK. You'll hear it in sentences like "Thank you" or "Thank you for bringing the drinks" — more examples below.
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1 syllable, 4 sounds. Explore each sound's mouth shape and how it's made.
Place the very tip of your tongue slightly between your teeth. Blow air gently around it without voicing.

Before NG, the vowel changes to sound more like the AY (/eɪ/) diphthong. The middle part of the tongue lifts toward the roof of the mouth, then the front part arches up.

Lift the back of your tongue to the soft palate. Lower your soft palate to let air flow through your nose.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Click any sentence to see the full breakdown — every link, every reduction, every flap-T.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "thank", the "a" vowel before NG shifts toward "ay" — sounding like "ay" as in "say", a distinctly American pattern — most prominent in Midwestern American English; other GenAm speakers may use a less raised vowel. Vowel changes to sound like /eɪ/ ("ay" as in "say").
In "thank", the "k" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.