All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

The tolerant Sharia of Islam has urged for glorifying Allah the Almighty at all times and in all situations and showed the great merit of this act. Abu Dharr reported: Some of the people from among the Companions of the Messenger of Allah (Peace and blessings be upon him) said to him: Messenger of Allah, the rich have taken away (all the) reward. They observe prayer as we do; they keep the fasts as we keep, and they give Sadaqa out of their surplus riches. Upon this he (the Holy Prophet) said: Has Allah not prescribed for you (a course) by following which you can (also) do sadaqa? In every declaration of the glorification of Allah (i. e. saying Subhan Allah) there is a Sadaqa, and every Takbir (i. e. saying Allah-O-Akbar) is a sadaqa, and every praise of His (saying al-Hamdu Lillah) is a Sadaqa and every declaration that He is One (La illha ill-Allah) is a sadaqa, and enjoining of good is a sadaqa, and forbidding of that which is evil is a Sadaqa." {Related by Muslim}.

It is permissible for a Muslim to count Tasbih on both hands, the right alone, the left alone or in any other way because there is no clear text that forbids counting Tasbih on the left hand. The Messenger of Allah commanded some women to count instances of Takbir (i. e. saying Allah-O-Akbar), Takdis (i.e. saying Glory be to the King, the Holy) and Tahllil (i.e. saying La illha ill-Allah) on fingers. Narrated Yusayrah, mother of Yasir: The Prophet (Peace and blessings be upon him) commanded them (the women emigrants) to be regular (in remembering Allah by saying): "Allah is most great"; "Glory be to the King, the Holy"; "there is no god but Allah"; and that they should count them on fingers, for they (the fingers) will be questioned and asked to speak." {Related by Abi Dawoud}. Here, the Hadith shows that the Tasbih isn`t restricted to the fingers of the right hand.

In this regard, we can say that the Messenger of Allah (Peace and blessings be upon him) used to like to start with the right in all his affairs. 'Aishah (may Allah be pleased with her) mentioned: "The Messenger of Allah (Peace and blessings be upon him) used to like to start with the right whenever he could, when purifying himself and when putting on shoes or combing his hair." (One of the narrators) Shu'bah said: Then I heard Al-Ash'ath in Wasit, saying that he liked to start with the right, and he preferred that in all his affaris. Then I heard him in Al-Kufah saying that he liked to start with the right whenever he could." {Related by An-Nasa`i}.

Since Tasbih is among the important matters, then, in principle, it should be counted on the right hand. The evidence on this is that Abdullah bin 'Amr (RA) said: "I saw the Prophet (Peace and blessings be upon him) counting the glorification of his Lord on his right hand." Ibn Qudamah said (in his version: "With his right hand" {Sunnan Abi Dawoud}.

Scholars of hadith said that "With his right hand" is Shaath (irregular) Hadeeth (the Hadeeth narrated by a trustworthy narrator but it differs from the narration of other trustworthy narrators (This difference may be either in Sanad [chain of transmission] or in Matan [text]). 

"It is disliked to count Tasbih on the left hand." {Moghni Al-Mohtaaj, V.1:378}.

In conclusion, there is no sin in counting Tasbih on both hands, the right alone or the left alone since this is just a way to keep the count, however, it is better to use the right hand. In addition, there is no need for disputing over this since preferring the right hand is merely guiding to what is best, but doesn`t mean that using the left isn`t permissible. And Allah the Almighty knows best.