verlegen
to move / reschedule
To move something to another place or to another time.
Können wir unseren Termin auf nächste Woche verlegen?
Can we move our appointment to next week?

to move / lay / misplace
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to move / reschedule
To move something to another place or to another time.
Können wir unseren Termin auf nächste Woche verlegen?
Can we move our appointment to next week?

'Verlegen' is an inseparable verb. The prefix 'ver-' always remains attached to the stem 'legen' and is not placed at the end of the sentence.
Er verlegt gerade das neue Laminat im Wohnzimmer.
He is laying the new laminate in the living room right now.
You can recognize the meaning of 'verlegen' from the object: you 'verlegt' an appointment (move/reschedule it), you 'verlegt' a key (misplace it), and you 'verlegt' a carpet (lay/install it).
Wir müssen das Treffen leider verlegen.
Unfortunately, we have to reschedule the meeting.
When you move or reschedule an appointment or event, use the preposition 'auf' followed by an accusative to indicate the new time.
Das Konzert wurde wegen des schlechten Wetters auf nächsten Monat verlegt.
The concert was moved to next month because of the bad weather.
In the context of construction work or renovations, 'verlegen' means to install something. Typical objects are cables, pipes, lines, tiles, or floor coverings such as carpet and parquet.
Ein Fachmann sollte die elektrischen Kabel verlegen.
A professional should lay the electrical cables.
This meaning is used for small personal objects that you put somewhere and then can no longer find. Typical examples are: 'die Brille verlegen' (to misplace one's glasses), 'den Schlüssel verlegen' (to misplace the key), or 'die Geldbörse verlegen' (to misplace the wallet).
Hast du mein Handy gesehen? Ich habe es anscheinend verlegt.
Have you seen my phone? I seem to have misplaced it.
When the subject is a publishing house ('der Verlag'), 'verlegen' always means 'publizieren' (to publish). It is then about the publication of books, magazines, or music.
Der Thienemann-Verlag verlegt viele bekannte Kinderbücher.
Thienemann Verlag publishes many well-known children's books.
to forget
'vergessen' and 'verlegen' are easy to confuse when you cannot find something anymore. 'vergessen' is more general: you no longer remember something, or you do not think of taking or doing something. 'verlegen' is used only for objects that you put somewhere and whose location you then no longer know. So you can forget an appointment, but you cannot 'verlegen' an appointment in this sense. And you can misplace a key because it is lying somewhere, but you do not know where.

Im Kurs habe ich meinen Stift verlegt und suche ihn seit zehn Minuten.
In class, I misplaced my pen and have been looking for it for ten minutes.
Zu Hause vergisst du oft, auf wichtige Nachrichten zu antworten.
At home, you often forget to reply to important messages.