Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
How to pronounce apologies in American English
Americans pronounce apologies as uh-PAH-luh-jeez (/əˈpɑlədʒiz/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "Please accept my apologies for any inconvenience this may have caused".
Now you try.
Record yourself saying "apologies" and play it back. The mic stays on your device — nothing's uploaded.
Every sound in "apologies".
4 syllables, 8 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 to stop the air, then release. No vocal cord vibration.

Relax your lips and drop your jaw significantly. The tongue tip lightly touches behind the bottom front teeth and the back part of the tongue presses down a little to create more dark space in the back of the mouth.

Place the tip of your tongue against the alveolar ridge just behind your top front teeth, the same contact point as /t/, /d/, and /n/. The difference is what happens to the air: for /l/, you let it flow continuously around the <em>sides</em> of the tongue (that's why /l/ is called a lateral). Turn your voice on the whole time. Lips stay relaxed, no rounding or flaring. For the Dark L variant at the end of a syllable, also pull the back of the tongue up and back toward the soft palate.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Touch the front of your tongue to the roof of your mouth, then release into a 'zh' position. Add vocal cord vibration.

Pull the corners of your lips back slightly. Arch the middle-front of your tongue high toward the roof of the mouth.

Same position as S, but add vocal cord vibration. Feel the buzz.

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Common pronunciation mistakes in American English.
The textbook way isn't wrong — it's just not how anyone actually says it.
Stressing the wrong syllable.
Stress falls on the second syllable, not the others. Stretch PAH — keep everything else short and quick.
Pronouncing the first syllable too fully.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.

