Afair six-sided die is rolled 6 times. what is the probability of getting all outcomes as unique?

You can do this step by step. 
First roll can be any and you can still get the correct outcome. 

Second roll has to be different from the first one, that is 5/6

3rd roll will have to be different from the last two, that is 4/6
And so on. 

Thus P=1*5/6*4/6*3/6*2/6*1/6, you can simplify this if you wish.