The sport that fits this criteria is "hockey." It has six letters, and the fourth letter is the letter "k." Hockey is a popular team sport played on ice or on a field, involving two teams who try to score goals by hitting a puck or a ball into the opponent's goal using a stick.
Hockey.
accentarrestattendbreechcaresscementdigestexpertexpectexpendextendforestindentintendinvestinjectparentpriestretestretellrevealrecessrepentresentrejectscreenstreamsleevespreadsleuthstressstreakthreadthreattalentunreal
rowing
Boxing
Tennis !
Hockey.
accentarrestattendbreechcaresscementdigestexpertexpectexpendextendforestindentintendinvestinjectparentpriestretestretellrevealrecessrepentresentrejectscreenstreamsleevespreadsleuthstressstreakthreadthreattalentunreal
iguana
testes
Diving
boxing
rowing
byacan or byacahn or byachan or pirranah
tinsel
Hockey.
Boxing
For a six-letter word to be a palindrome, the 3rd and 4th letters would have to be the same.