The "door-in-the-face" technique is when someone asks you for something big or unreasonable first, and then asks you for something smaller or more reasonable in comparison. This is done in the hopes that you will feel more inclined to say "yes" to the smaller request after being asked for something bigger.
For example, a salesperson may ask you to buy a very expensive car first, knowing that it's too expensive for you, but then ask if you would be interested in a cheaper model. The cheaper car seems more affordable and reasonable after being asked for something much more expensive first.
The "door-in-the-face" technique can also work in everyday situations. For instance, if your friend wanted to borrow $100 dollars, but you really didn't want to lend them that amount, they may then ask to borrow $20 dollars instead. You may feel like you can say "yes" to the smaller request after being asked for something much larger previously.
Remember that this technique is a persuasion tactic, so be aware of when it is being used on you and decide if you really want to agree or not.