Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

Americans pronounce tanker as TANG-ker (/ˈtæŋkər/). In "tanker", 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, and it's one of the defining features of casual American English. It comes out as TANG·ker. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The driver drove the tanker to the center".
Record yourself saying "tanker" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 5 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

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.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "tanker", 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 TANG — keep everything else short and quick.
Americans use a relaxed retroflex R — the tongue curls back rather than rolling. The R is one continuous sound with the vowel before it, not two separate sounds.