Both sentences are correct.

[Jessica725]

1.Both sentences are correct.
2.I like both cats.
3.I know both her children.
4. Both of my friends are studying in Japan.
Are these sentences correct?

 

[5jj]

All your sentences are correct, assuming you are talking about two sentences/cats/children/friends.

Note that I have changed the title of your thread. Titles should give us some idea of what the thread is about.

 

[emsr2d2]

Are these sentences correct?

1. space here Both sentences are correct.
2. space here I like both cats.
3. space here I know both her children.
4. Both of my friends are studying in Japan.

Note my change of layout and added spaces above. They're all grammatically correct but #4 is a bit unlikely unless you really have only two friends.