She clean forgot to tell me her address before leaving. Here 'Clean' is a/an -

The correct answer is option 2), i.e. Adverb.
An adverb is a word that modifies a verb, adjective, or another adverb. 
Example: They are extremely poor.
In the given sentence 'clean' is used before the word 'forgot' to express the meaning 'completely'.
It has modified the verb 'forgot'. 
So, it is an adverb. 
Ex:
The bullet went clean through his shoulder.
I clean forgot that I was supposed to be meeting Lucy last night.

'Clean' is also used as an adjective. 
It means 'washed' or 'free from dust or dirt'. 
Example: Her dress is clean. 
'Clean' is also used as a verb. 
It means 'to wash'. 
Example: You should clean your bag.