The narration about the Prophet (saw) counting Tasbih on his right hand… [Reported by Abu Dawud]
The extra wording “his right hand” is weak as it was singularly narrated by Muhammad b. Qudāmah and he opposed the other Huffadh (reliable narrators) that narrated this hadith without the extra addition.
Based on this, a person can count his Tasbih on his right and left hand.
– Sh. Bakr Abu Zayd (r)