Units Digit :
Lets take the first part of the problem :
i.e. 2467^163..
Unit place of 2467 is 7, thus for powers of 7 the units place can be the following :
7
9
3
1
and then the cycle repeats..
Hence the power of 7 pertains to a 4 number cycle, divide the required power 163 by 4
163/4 leaves a reminder 3 hence from the cycle above the unit digit is 3.
Now the second part..
341^72
The unit digit of any power of 1 is again 1..
Thus 341^72 unit digit is 1.
Now multiply both the unit digits (3*1) = 3.
Thus the unit digit of the expression 2467^163 * 341^72 is 3.
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