Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Americans pronounce suggests as suhg-JEHSTS (/səgˈdʒɛsts/). In "suggests", the "t" is squeezed between other consonants and drops out — the surrounding consonants flow together without it — most natural in flowing, casual speech; in careful or formal speech, the T may be lightly present. This is called the Silent T in Clusters, a small move that separates 'classroom' from 'native'. It comes out as suhg·JEHSTS. Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "The data suggests a positive outcome" or "Much research suggests a rich future approach" — more examples below.
Record yourself saying "suggests" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 8 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Raise the back of your tongue to touch the soft palate. Add vocal cord vibration, then release.

Touch the front of your tongue to the roof of your mouth, then release into a 'zh' position. Add vocal cord vibration.

Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

The T is skipped entirely. Your tongue doesn't make contact at the T position.

Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

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 "suggests", the "t" is squeezed between other consonants and drops out — the surrounding consonants flow together without it — most natural in flowing, casual speech; in careful or formal speech, the T may be lightly present. /t/ is dropped entirely — the surrounding consonants flow together without the T.
In "suggests", the "t" 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 second syllable, not the others. Stretch JEHSTS — 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.