Why it is considered good to see ones own palms after waking up in the morning which we follow in hindu dharma also old people advise the same
It has actually nothing to do with astrology (you originally tagged your question with it).
At various portions of our palms are present various Hindu Gods. That's why it's auspicious to see our palms immediately after waking up in the morning. The act is supposed to make the upcoming whole day fruitful, auspicious etc for us.
The Nitya Karma PujA PrakAsh Book (on pp 19) mentions the following sloka:
KarAgre vasate lakshmih karamadhye saraswati |
Karamule stitho brahmA prabhAte karadarshanam ||
At the tips of the palms resides Lakshmi, at the middle Saraswati and at the base of the palms resides BrahmA, that's why we need to see our palms at early morning.
This sloka is actually from the Vishnu PurAna as shown in this answer.