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

Americans pronounce manufacturing as ma-nyoo-FAK-cher-uhng (/ˌmænjəˈfæktʃərəŋ/). In "manufacturing", the "a" vowel before M or N raises and fronts toward [eə] — the tongue pulls up and forward, breaking the vowel into a tense glide as it anticipates the nasal. This is called the Cat-Vowel Before M/N, the kind of sound shift that makes everyday speech feel effortless. It comes out as MA·nyoo·FAK·cher·uhng. Stress falls on the third syllable — keep everything else short and quick. You'll hear it in sentences like "The manufacturing sector is facing supply chain disruptions" or "Automation is expected to replace numerous jobs in manufacturing" — more examples below.
Record yourself saying "manufacturing" and play it back. The mic stays on your device — nothing's uploaded.
5 syllables, 11 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Press your lips together. Air flows through your nose. Vocal cords vibrate.

The tongue relaxes down in the back and the corners of the lips relax before the consonant. This adds a schwa-like 'uh' relaxation after the /æ/. Think of it as 'relaxing out of the vowel' — it is no longer a pure /æ/ sound.

Lift your bottom lip to touch the very bottom of your top front teeth. Blow air through this contact point without voicing.

Drop the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

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 "manufacturing", the "a" vowel before M or N raises and fronts toward [eə] — the tongue pulls up and forward, breaking the vowel into a tense glide as it anticipates the nasal. The "/æ/" vowel raises and fronts before M or N — tongue pulls up and forward, producing a tense [eə] glide (between /e/ and /ə/). Not a pure /æ/.
In "manufacturing", 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.
Stress falls on the third syllable, not the others. Stretch FAK — keep everything else short and quick.
Don't pronounce the fourth syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.