1
Both of them didn’t pass the exam.
Neither of them passed the exam.
Do not use both … not when you mean ‘not one and not the other’. Use neither.
2
I want to buy these both books.
I want to buy both these books.
I want to buy both of these books.
She really missed her both daughters.
She really missed both her daughters.
She really missed both of her daughters.
Use both or both of before the, these, those or a possessive such as my, your or her.
3
Both we love horror films and popcorn.
We both love horror films and popcorn.
Both of us love horror films and popcorn.
With a subject pronoun, use we/you/they + both or both of + us/you/them.
4
We both were invited.
We were both invited.
They both have gone home.
They have both gone home.
When both refers to the subject, it normally goes in mid position: before the main verb, but after the verb be and after the first auxiliary verb.
5
They invited we both.
They invited us both.
They invited both of us.
After a verb, use us/you/them + both or both of + us/you/them. Do not use the subject pronouns we or they here.
See ALL (3, 4, 5)