anbieten
to offer
To make something available to someone for purchase, use, or consumption.
Darf ich Ihnen ein Stück Kuchen anbieten?
May I offer you a piece of cake?

to offer
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to offer
To make something available to someone for purchase, use, or consumption.
Darf ich Ihnen ein Stück Kuchen anbieten?
May I offer you a piece of cake?

'Anbieten' (to offer) is a separable verb. The prefix 'an-' goes at the end in main clauses, but remains attached to the verb in subordinate clauses. In the infinitive, 'zu' comes between 'an' and 'bieten'.
Er bietet seinen Gästen immer Wein an.
He always offers his guests wine.
This verb is very often used with two objects. The person receiving the offer is in the dative, and the thing being offered is in the accusative.
Mein Kollege hat mir seine Hilfe angeboten.
My colleague offered me his help.
When a person 'sich anbietet' (offers themself), it means that they voluntarily make their help available. It is often followed by an infinitive construction with 'zu' that describes the activity.
Ein freundlicher Herr bot sich an, meinen schweren Koffer zu tragen.
A friendly gentleman offered to carry my heavy suitcase.
When a situation or thing 'sich anbietet' (suggests itself), it means that it represents a good opportunity. The subject here is not a person actively helping, but the opportunity itself.
Da wir schon in der Stadt sind, bietet es sich an, auch gleich einzukaufen.
Since we're already in town, it makes sense to do the shopping right away too.
to lead
'führen' and 'anbieten' can both mean that a business has certain goods or services. 'führen' sounds more like the regular range: 'Ein Laden führt eine Marke oder ein Produkt' (a shop carries a brand or product). 'anbieten' puts more emphasis on something being available to customers, for purchase or use. The words can be confused because both fit in shops and services. If you want to say what is permanently in the product range, 'führen' works well. If you want to show what customers can get, 'anbieten' is more natural.

Sofia bietet den Gästen Kaffee und Kuchen an.
Sofia offers the guests coffee and cake.
Der Supermarkt führt diese Teesorte nur im Winter.
The supermarket carries this type of tea only in winter.