Eg: if player 1 has 444 full of AA and player 2 has 888 and 44 , which is best hand , highest card or highest trips ?
The winner is the player with the highest trips, so 88844 is the winning hand.
If you use the search term "Full House" then you should find a few more decent examples here to explain the concept.
Also, check out the "five card rule" for a definitive overview of Texas Hold Em hand rankings.
The winner is always the best 5-card hand. So, in the case of a Full House, it goes by the 3-of-a-kind first, then the pair.
444AA vs.88844 888 is higher than 444, so ‘88844’ is the high hand here. The only time the pair matters is if both players have the same 3-of-a-kind. For example:
444AA vs. 44488 (444 is on the board, Player 1 has pocket AA, Player 8 has pocket 88). Since both players share the 444, the tie-breaker is the pair they use. AA beats 88, so Player 1 would win here having 444AA as their best 5-card hand.