
mitbekommen
to notice
To notice, perceive, or find out about something, often incidentally or by chance.
Hast du mitbekommen, dass unsere Nachbarn ein neues Auto haben?
Did you notice that our neighbors have a new car?
to notice / understand / get
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to notice
To notice, perceive, or find out about something, often incidentally or by chance.
Hast du mitbekommen, dass unsere Nachbarn ein neues Auto haben?
Did you notice that our neighbors have a new car?

to understand
To understand something in terms of its content or grasp it mentally.
Ich habe die Anweisungen nicht richtig mitbekommen, kannst du sie wiederholen?
I didn't really understand the instructions; can you repeat them?

to get
To receive something to take along, often as a gift, provisions, or for a specific purpose.
Jeder Gast hat zum Abschied eine kleine Flasche Wein mitbekommen.
Each guest got a small bottle of wine to take home as they left.
'Mitbekommen' (to notice / understand / get) is a separable verb. The prefix 'mit-' goes to the end in main clauses. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Ich bekomme von dem Lärm draußen kaum etwas mit.
I can barely hear anything of the noise outside.
The verb is made up of 'mit' (with/along) and 'bekommen' (to get). The prefix 'mit-' suggests that you receive something additionally or incidentally—whether it is information, understanding, or an object.
Er hat nur am Rande mitbekommen, worüber sie gesprochen haben.
He only vaguely picked up what they were talking about.
When 'mitbekommen' (to get) has a concrete, physical object as its accusative object, it almost always means 'to receive something to take along'. The other meanings refer to abstract things like information or understanding.
Für die lange Fahrt haben wir von unseren Gastgebern Sandwiches mitbekommen.
For the long trip, our hosts gave us sandwiches to take along.
to get / receive
Bekommen simply indicates that someone receives an object. Mitbekommen can also describe receiving something, but additionally says that it is handed over to be taken along. Before a departure, mitbekommen is appropriate when this purpose is important.

Vor der Reise bekam Mia von ihrer Mutter eine Decke mit.
Before the trip, Mia was given a blanket by her mother to take along.
Vor der Reise bekam Mia von ihrer Mutter eine neue Decke.
Before the trip, Mia got a new blanket from her mother.