
abwickeln
to process
To carry out and complete a process, transaction, or task according to plan.
Die Bezahlung wird komplett online abgewickelt.
The payment is processed completely online.
to process / unwind / liquidate
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to process
To carry out and complete a process, transaction, or task according to plan.
Die Bezahlung wird komplett online abgewickelt.
The payment is processed completely online.

to unwind
To unroll or unwind something that is rolled up or wound up.
Sie wickelte den Verband vorsichtig vom Arm ab.
She carefully unwound the bandage from her arm.

to liquidate
To dissolve a company or organization and settle its remaining business and finances.
Nach der Insolvenz musste das Unternehmen abgewickelt werden.
After the insolvency, the company had to be liquidated.
'Abwickeln' (to process/unwind/liquidate) is a separable verb. The prefix 'ab-' separates from the verb in a main clause and stands at the end. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Die Firma wickelt das Geschäft schnell ab.
The company processes the transaction quickly.
You can recognize the meaning of 'abwickeln' from the object. If it is a physical object such as a rope or thread, the literal meaning 'abrollen' (to unroll) is meant. With abstract things such as a transaction, a purchase, or a company, it is about the figurative meaning 'durchführen' (to carry out/process) or 'auflösen' (to dissolve/liquidate).
Der Elektriker wickelt das Kabel von der Rolle ab.
The electrician unwinds the cable from the reel.
In a business context, 'abwickeln' (to process) is often combined with financial or organizational processes. Typical phrases are 'einen Kauf abwickeln' (to process a purchase), 'eine Transaktion abwickeln' (to process a transaction), or 'den Zahlungsverkehr abwickeln' (to handle payment transactions).
Der gesamte Bestellprozess wird online abgewickelt.
The entire ordering process is handled online.
The meaning 'eine Firma auflösen' (to dissolve/liquidate a company) belongs to business and legal language. It describes the formal process of closing a company.
Der insolvente Konzern wird von einem Spezialistenteam abgewickelt.
The insolvent corporation is being liquidated by a team of specialists.
to carry out
Durchführen and abwickeln can both describe a process or task carried out according to plan. Durchführen focuses on the execution, while abwickeln additionally emphasizes the orderly process through to completion. Use „durchführen“ when implementation is important and „abwickeln“ when a process is to be completed in full.

Die Mitarbeiterin wickelt die Bestellung bis zum Versand vollständig ab.
The employee is processing the order completely, through to shipping.
Die Mitarbeiterin führt die Bestellung nach den neuen Regeln durch.
The employee is processing the order according to the new rules.