If you are not going to include the last day in your computations, it will be like this:

First, we will subtract the latest year to the given starting year.
1999-1996= 3 years

In days, these three years will count as:
 \frac{3 years}{} * \frac{365 days}{1 year} =1095 days

However, we should consider the dates where there had been leap years. 
Since leap years tend to happen every four years, and 1996 is divisible by 4, that means we had a leap year on 1996. So we should add 1 from 1095, and we get 1096 days.

Then, we will subtract the latest month to the previous month.
Since we're working in 1999 now, we will not be bothering with leap years on February.

I'm just doing this by observation, so if anyone knows a better way, please post it here. 

Since we're dealing from February to April, we could just add up the amount of months on the other months in the middle.

March has 31 days so we will add it to our previous answer, and we will get 1127 days.

Now, we subtract.
In February, in order to get to the next month on the same day, you need 28 days. (if it's not a leap year)
Since the dates were 16 and 9 and the difference of those two numbers are 7, it must mean that it was not able to get to a cycle of a February month of 28 days. 

So, we subtract 7 from 28 and we get 21.

Finally, we will add 1127 and 21 and we will have the final answer of 1148 days.
If you need to include the last day, April 9, 1999, you just have to add one day.
And if you need to convert them to other units of measurement, just remember that:

There are 24 hours in a day.
60 minutes in an hour, and
60 seconds in a minute.
I hope that helps. 
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