Correct spelling

preferably

Correct spelling, explanation: preferably is the correct form as it comes from the verb prefer, which ends with one r. There is no need to double the last consonant if the last syllable (the syllable with suffix) isn’t stresed. Therefore prefer + -able = preferable, and then adverb is made by adding another suffix: -ly. Therefore preferably is the correct form and preferrably is incorrect.

Definition of preferably:
adverb, in a preferable manner
We are looking for a bigger flat; preferably with 5 bedrooms.
Complaints should preferably be addressed to the management department.


Incorrect spelling

preferrably

Incorrect spelling, explanation: there is no reason to double the consonant r in preferably, so preferrably is an incorrect spelling. The correct form, preferably, comes from adjective preferable which is created by verbs prefer and suffix -able. The suffix syllable isn’t stressedl so r in prefer isn’t doubled.