Assalamualaikum wa rahmatullahi wa barakatuh,
I wanted to ask as I am seeing different things on the issue, regarding wudu, when washing the hands, how is the method of washing the hands during wudu done?
One place I read we wash the right hand three times first, then the left hand three times. Another one told me I can wash them both at the same time three times.
For it to count three times, I have to pour water over my hands through the sink three times, by removing my hands from the pouring water three times (so that it'll count three times).
Which one is correct?
Jazakallah Khayran.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

If what you meant is washing your hands up to the wrist at the beginning of ablution, as it appears to us, then you should know that washing them at the beginning of the ablution is only recommended and not obligatory.

Ibn Al-Munthir said in his book Al-Awsat: "All scholars from whom we have learned agreed unanimously that washing the hands at the beginning of ablution is a Sunnah that is recommended to act upon. One has the choice to wash them once, and if he likes he may wash them twice, or if he wishes he may wash three times; one can choose whatever he likes from these options. However, I would prefer washing them three times." [End of quote]

The scholars differed on how to wash the hands in order to coincide with the Prophetic Sunnah. Does one wash each one separately by washing the right hand three times first and then washing the left hand three times? Or does one wash them together three times? Washing them separately was reported by Ash'hab from Imam Maalik. Ibn Al-Qaasem is of the opinion that it is better to wash them together, and one has the choice to follow any of these two opinions.

If you wash them together under the faucet, then every time you remove your hands from under the flow of water, this will count as one washing. Doing this three times will count as washing them three times.

Allah Knows best.