If we round off $7,14,68,914$ to nearest thousands, we get:

Given:

The number $7,14,68,914$.

To round off the given number to nearest thousands we will check the digit at hundreds place. If the digit at hundreds place is less than $5$, then the digit at thousands place will remain same. If the digit at hundreds place is more than $5$, then we will add $1$ to the digit at thousands place. The last three digits that are the hundreds, tens and ones place will be $0$.

In the given number, the digit at hundreds place is $9$, which is more than $5$, so we will add $1$ to the digit at thousands place that is $8$ and the last three digits that are the hundreds, tens and ones place will be $0$.

So, the number will be $7,14,69,000$.

Hence, option A is correct.