Both is used to talk about two people or things.

Both cats and dogs are pet animals.

Before a noun with a determiner (the, my, this stb.), both and both of are both possible.

Both of my parents are teachers. VAGY Mindkét szülőm tanár.
Az ingek közül mindkettőt veheted. VAGY Elveheted mindkét inget.
Mindkét válasz helyes. VAGY Mindkét válasz helyes.

Note that the is often dropped after both.

She has eaten both chops. VAGY She has eved both the chops. VAGY She has eaten both of the chops.

A személyes névmások előtt a both of-t használjuk.

Both of them have agreed to come. (NOT Both them have agreed to come.)
She has invited both of you. (NOT She has invited both you.)

Note that both of is followed before the object forms of the pronoun (us, them, you etc.).

The not used before both

We do not put the before both.

Both the boys were given prizes. (NOT The both boys were given prizes.)

Negatív szerkezetek

A negatív szerkezetekben a neither, not both not-t használjuk.

Neither of them came. (NOT Both of them did not come.)

Both with verbs

Note the special structure in which both goes with the verb.

They can both swim. (= Mindketten tudnak úszni.)
They have both come. (= Mindketten eljöttek.)
Mindkettőjüknek tetszett a film. (= Both of them liked the movie.)

Both…and

Note that in this structure words of the same part of speech follow both and and.

She is both beautiful and intelligent. (Itt a both and és után melléknevek következnek.)
She both sings and acts. (Igék)
Meghívtam Jánost és Pétert is. (Főnevek)