Is this a acceptable ghusl first I start with niyyah and than rinse my mouth and nose three times and than take a shower making sure the water covers my entire body.
This is a valid ghusl as it meets the conditions for validity of ghusl.
According to Ĥanafī fiqh, ghusl consists of three obligatory act, and if one is omitted then the ghusl is invalid:
- To rinse the mouth
- To cleanse the nose
- To wash the entire surface of the body
Imām Abu’l Ĥusayn Aĥmad al-Qudūrī al-Ĥanafī [362-428 AH / 973-1037 CE] writes in his Mukhtaşar:
Intention is not needed in order for ghusl to be valid according to Ĥanafī fiqh, if you follow another madh'hab, please inform so the answer can be provided accordingly.