The least positive digit $x$, so that the number $324x342$ is divisible by 11 is:

For a number to be divisible by 11, the difference between the sum of digits at odd places and the sum of digits at even places must be either 0 or a multiple of 11.Given number: $324x342$ Sum of digits at odd positions (from right to left: 1st, 3rd, 5th, 7th):
$$S_{\text{odd}}=2+3+4+3=12$$
Sum of digits at even positions (2nd, 4th, 6th):
$$S_{\text{even}}=4+x+2=6+x$$
Find the difference:
$$\text{Difference}=S_{\text{odd}}-S_{\text{even}}=12-(6+x)=6-x$$
For divisibility by 11, this difference should be 0:
$$6-x=0⟹x=6$$