So in Texas holdem if two players have a straight with the same card who wins, (one player has a pair of 6s and the other player has a king)??
In Texas Hold'Em you use the strongest five-card hand that can be made using your two in-hand cards and the 5 board cards. The two cards that you do not use are ignored completely and have no effect on the hand rankings. (This is similar to 7-card stud and other 7-card variants)
In the example you present, it sounds like each player has an identically-ranked straight as their best five cards. The pair of sixes would be ignored, as would the high-card king. This would be a tie and the two players would split the pot.
In Texas Hold'em you construct the best 5 card hand you can out of the 7 cards available. The cards not included in the hand have no bearing on the winning or losing of any individual.
For the scenario you described, if both players have straights and that are made up of the same set of cards and neither has a straight flush, then it is a tie and the pot is split.