Correct spelling


Correct spelling, explanation: this is an example of using the rule of consonant-vowel-consonant ending of the word. In such cases, whenever a suffix is added, we double the last consonant. Since the word transfer ends with this combination we double the last r with suffix -ing, therefore transferring is the correct form. Transfering is a misspelling.

Definition of transferring:
verb, -ing form of transfer; to remove (usually a person) to another place, for example other school or workplace
They are transferring me to another department at work and I’m pretty excited.
Mary’s parents are thinking about transferring her to another school.

Incorrect spelling


Incorrect spelling, explanation: transfering is a mistaken form, because the word transfer ends with a combination of consonant-vowel-consonant. In such case we double the last consonant when adding any suffix. Therefore here the correct form will be transferring.