nebenan
next door
Refers to a place located directly next to another one, for example the neighboring house, apartment, or room.
Das Zimmer nebenan ist noch frei.
The room next door is still available.

next door
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next door
Refers to a place located directly next to another one, for example the neighboring house, apartment, or room.
Das Zimmer nebenan ist noch frei.
The room next door is still available.

The word 'nebenan' (next door) is made up of the words 'neben' (next to) and 'an' (on/at). It literally means 'directly next to it' and is used for places like the neighboring house or room.
Die Bäckerei ist gleich nebenan.
The bakery is right next door.
'Nebenan' (next door) is an adverb and is not declined like a normal adjective. It either stands alone or after the noun it describes. A form like 'das nebenane Haus' is incorrect.
Meine Großeltern wohnen nebenan.
My grandparents live next door.
A very common and useful phrase is 'die Nachbarn von nebenan' (the neighbors next door). It refers to the people who live in the house or apartment directly next to you.
Gestern habe ich meine neuen Nachbarn von nebenan kennengelernt.
Yesterday I met my new neighbors from next door.
next to / besides
'neben' and 'nebenan' both have to do with a place directly at the side. The difference is in how they are used. 'neben' is a preposition and usually needs a noun after it, for example 'neben dem Tisch' (next to the table) or 'neben die Tür' (next to the door). 'nebenan' describes a neighboring place, often the next apartment, the next room, or the house next door. So you do not say 'nebenan dem Tisch', but 'neben dem Tisch'. Learners easily confuse the words because both express spatial closeness. If you are saying exactly which thing something is next to, use 'neben'. If you mean the place next to the current place, use 'nebenan'.

Die Kinder spielen nebenan, deshalb ist es im Wohnzimmer laut.
The children are playing next door, so it is loud in the living room.
Frau Klein stellt die Tasche neben den Stuhl.
Ms. Klein puts the bag next to the chair.