Correct spelling


Correct spelling, explanation: completely is an adverb from the adjective complete. To create an adverb we add suffix -ly to an adjective, so complete + -ly is completely. Therefore completly is incorrect – there is no need to skip e.

Definition of completely:
adverb, totally, thoroughly, in a complete matter
I completely agree with Jim. We should take up this project.
They have taken mortgage for a villa? They must be completely insane! They can’t afford it.

Incorrect spelling


Incorrect spelling, explanation: this form is incorrect, because adding suffix which begins with a consonant, to a word ending with e doesn’t require skipping the e. So, by adding adverbial suffix -ly to the adjective complete we get the word completely, not completly. We don’t skip the e, so completely is the correct form.