My B1/B2 visa expires on August 14, and I have to stay in the US from August 14 to 17. I want to apply for a new visa for these dates. Will the embassy give me a new visa or they will ask me to travel with the same visa?
For most countries, the visa must be valid for the entire duration of the stay. The US treats things differently; as this answer says:
A US [...] visa's expiration date only means the last day on which you can use the visa to enter the US. A visa has no bearing on your ability to stay in the US -- that is determined by the Admitted Until date on your I-94.
Although the paper I-94 has gone the way of the dinosaurs, the same is still true of the admission stamp in your passport (and the corresponding electronic I-94 record).
So: you can lawfully use your existing visa to enter the US on 14/8 and leave on 17/8. It might raise the odd eyebrow on entry, but it's perfectly lawful. Therefore, although we can't predict what the embassy will do, they might well point out that you don't need a new visa to make the journey as planned, and hence decline to issue you one. I also doubt (though I admit I'm unsure) that you can have two B visas with overlapping validity periods, so being issued a new one will implicitly involve cancelling the old one. Whilst this is normal, there are few interactions with US immigration authorities that are improved by having a visa cancellation in your history, so this is something to avoid if possible.
Is there any particular (unstated) reason that you want to apply for a new visa? As I see it, you might as well save yourself the money and hassle.
As a general rule, the US will not allow you to have multiple visas of the same type running concurrently.
However all this means is that once your new B1/B2 visa is approved, they will cancel your existing visa by stamping over it with "Canceled Without Prejudice". The "Without Prejudice" here refers to the fact that the visa wasn't canceled due to (for example) you breaching the conditions, but simply because they issued a new overlapping visa.
You new visa will start on the day of issue, and thus will cover the period of your trip.
Technically you don't need to apply for a new visa for the trip you've described. Unlike many other countries, the expiry date on a US visa is actually the date that you need to ENTER the country, not the date you need to leave - thus it would actually be possible to use your existing visa to enter on the August 14, at which point you would be given "status" that would allow you to stay within the US for (normally) 6 months. It doesn't matter that your visa would have expired by that time - as long as you enter the country by the expiry date you're good.
That said, I would NEVER plan to enter the country on the last day of a visa's validity. All it would take is a flight delay/cancellation and you'll find yourself in a situation where you will be entering after the 14th. In that case, you can expect to be denied boarding for your (rescheduled) flight on the grounds that you don't have a valid visa, or potentially refused entry into the US if you do happen to make it there.