Correct spelling


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 stressed. Therefore prefer + -able = preferable, and then an 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


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 the adjective preferable which is created by the verbs prefer and suffix -able. The suffix syllable isn’t stressed so r in prefer isn’t doubled.