Check what really happened
Look at the payment record first. Two charges, one charge plus a pending authorisation, and a charge from a duplicate account look alike to the customer and need different answers.
Refund a real duplicate straight away
Do not make them prove it. Refund the extra charge, say how long the bank usually takes and give the refund reference.
Explain a pending hold plainly
If it is an authorisation, say it will drop off by itself and roughly when. Offer to check again if it has not gone after that date.
Say sorry once and be specific
Name the amount and the date. Skip long apologies and explain in one sentence what went wrong, if you know.
Find the cause and fix it
Tag the ticket. Repeated double charges point to a retry bug, a double click on checkout or duplicate accounts, and each has a different fix.