Push a stream of air from your throat through your open mouth. No tongue or lip contact.

Americans pronounce hearts as HARTS (/hɑrts/). It's 4 sounds in 1 syllable. The R curls back and blends into the vowel — they sound as one continuous unit.
Record yourself saying "hearts" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 4 sounds. Explore each sound's mouth shape and how it's made.
Push a stream of air from your throat through your open mouth. No tongue or lip contact.

Open wide for the 'ah' vowel. Lift the tongue back and up while flaring the lips for the 'r'.
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.

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.
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.