Question:Requred digit 

=unit digit in the product `(4 xx 8 xx 7 xx 3)`=2

Question:`9 xx 6 xx 4`216. 

In order to obtain 2 at the unit place it must be multiplied by a number whose unit digit is 7.
So,*must be replace by 7.

Question:Unit digit in `7^4`is 1.` 

:.Unit digit in `7^68`is 1.

 :.Unit digit in `7^71`is 3. `[1 xx 7 xx 7 xx 7` gives unit digit 3]

 Again,every power of 6 will give unit digit 6.

 :. Unit digit in `6^59` is 6.

 Clearly,unit digit in `3^4` is 1.

 So,unit digit in `3^64` is 1

 :.Unit digit in `3^65` is 3.

 :. Unit digit in `(7^71 xx 6^59 xx 3^65)` is 4. `[3 xx 6 xx 3`gives unit digit 4]`

Question:Unit digit in the given product=unit digit in `7^153 xx 1^72`. 

Now `7^4`gives unit digit 1.
:.`7^152` gives unit digit 1.
:.`7^152` gives unit digit `(1 xx 7)=7`
Also `1^72`gives digit 1.
:.Unit digit in the product =`(7 xx 1)=7`.

Question:Unit digit in `7^4` is 1` 

So,unit digit in `7^92` is 1.
:.Unit digit in `7^95` is 3.   [:. Unit digit in `1 xx 7 xx 7 xx `is 3 ]
Unit digit in `3^4`is 1
:. Unit digit in `3^56` is 1.
:. Unit digit in `3^58` is 9. [:.Unit digit in `1 xx 3 xx 3 xx` is 9]
:. Unit digit in `(7^95 - 3^58)` is 4.[Subtracting  unit digit 9 from unit digit]

Question:`4^11 xx 7^5 xx 11^2` 

=`(2 xx 2)^11 xx 7^5 xx 11^2`
=`2^11 xx 2^11 xx 7^5 xx 11^2`
=`2^22 xx 7^5 xx 11^2`.
:.The number of prime factors is (22 + 5 + 2)=29