villain has a button 3bet of 10.6 so i figure my hand, given our positions is an easy 4bet, get it in.  

now I am not completely sure what range I can put him on on the turn. when he flats my 4bet in position pre i put him on something kinda speculative like a suited connector or pre flop trap. given i picked up equity with my king high flush draw i really wanted to shove but i couldnt think of any hands that i could get to fold by shoving. so i check and it goes check check and i check give up to a river shove. 

I was pretty lost for most of this hand and probably made some mistakes, I think i should have shoved turn incase hes floating flop with some 87 or 67 or maybe if he played a mid pair weird and 3bet called one of them maybe i can get one of them to fold. Also there is a chance he had some 45 or 56 suited that rivered a boat that i could have folded out on the turn. 

thoughts are much appreciated .