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

Americans pronounce gymnastics as jihm-NA-stihks (/dʒɪmˈnæstɪks/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "She won the gold medal in gymnastics for her floor routine".
Record yourself saying "gymnastics" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 10 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
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 slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

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

Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

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.

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

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.

Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

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

The textbook way isn't wrong — it's just not how anyone actually says it.
Stress falls on the second syllable, not the others. Stretch NA — keep everything else short and quick.