The smallest $8-$digit number using the digits $7,0,6,5,4,3$ (repetition is allowed) will be:

Given:

The digits $7,0,6,5,4,3$.

Let us first make the place value chart.

To make the smallest $8-$digit number, we will select the smallest digit that is $0$, but if we start a number with $0$, it will not be a $8-$digit number. So, we will take the second smallest digit that is $3$ and place it at crore's place and then we will place $0$ at ten lakh's place.

As the digits given is only $6$, so we will repeat $0$ twice as repetition is allowed to make the number of $8-$digit.

Now we will arrange the remaining digits in increasing order (smallest to greatest) as below, to get the required number.

So, the required number is $3,00,04,567$.

Hence, option B is correct.