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

Americans pronounce thanking as THANG-kuhng (/ˈθæŋkəŋ/). In "thanking", 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, a small move that separates 'classroom' from 'native'. It comes out as THANG·kuhng. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "She made a beautiful speech thanking everyone for their support".
Record yourself saying "thanking" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 6 sounds. Tap a syllable to jump to its row, then 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.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Lift the back of your tongue to the soft palate. Lower your soft palate to let air flow through your nose.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "thanking", 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").
Stress falls on the first syllable, not the others. Stretch THANG — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.