Hello and welcome to the PlayStation Forums, haijang2.
If you're asking if the PlayStation Vita can play PlayStation 4 video games, it all depends on which game that uses the Remote Play feature.
Here's more info regarding Remote Play with the PS4 & Vita
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Yes it can, via remote play.
A little bit from the article:
Additionally, Sony has announced that all PlayStation 4 games will be playable on the PlayStation Vita. Beyond these two scenarios, Remote Play was a feature that was sparingly implemented in games.
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Playstation customer support numbers: 1-877-971-7669 (for billing and Playstation Network); 1-800-345-7669 (for technical support)
The PlayStation Vita has the ability to play multiplatform games that also appear on the PlayStation 4. The following are some of the games available (or will be) for both platforms:
Soul Saga: Episode I
The Walking Dead
The Walking Dead: Season 2
The Wolf Among Us
PixelJunk Shooter Ultimate
You can also play PlayStation 4 games remotely with the Vita. Not all games have access to this function, but there should be many that permit it. With remote play you essentially have the ability to take the game you're playing on your TV screen and wirelessly transfer it to the portable hardware for on-the-go accessibility. Since it's like trying to transmit a reception on a radio directly from the main source (your PlayStation 4 console), you may or may not always get a strong signal. Though, it's probably not as hopeless as the situation may seem.
I just remote play everything when I want to use my Vita, which is especially useful if you're living in a dorm or with anyone else and it's late at night. Granted, not all titles allow Remote Play, but I enjoy my time with those that do.
That, and it makes me feel like my Vita can do more than collect dust.