The sum of the digits in the unit's place of all the 4-digit numbers formed by using the numbers 3, 4, 5 and 6 without repetition is 

The given digits are $3,4,5,6$

The unit digits in any of four digit numbers  formed by $3,4,5,6$ is one of $3,4,5,6$$3+4+5+6=18$

The number of four digit numbers having 3 as in unit digit is $3!$

The number of four digit numbers having 4 as in unit digit is $3!$

The number of four digit numbers having 5 as in unit digit is $3!$

The number of four digit numbers having 6 as in unit digit is $3!$

Hence, the sum of the unit digits of all the 4-digit numbers formed by using the numbers 3, 4, 5 and 6 without repetition is $\left(3+4+5+6\right)\left(3!\right)=18\left(6\right)=\boxed{108}$