I’m twice your age. [OED]
It looks like ‘twice’ is a preposition to me, yet it’s an adverb. On what procedure do you think in your brain, can this be an adverb?
You can make an argument that it is an adverb:
In the sentence "I am your age", the word "am" expresses a relationship between the subject "I" and the phrase "your age". If I insert the word "twice", it modifies "am", changing the relationship between them. I don't think this works particularly well; I feel like "twice" modifies the following phrase, instead. If I say "I am twice", I ask, "Twice what?" It feels incomplete.
I think it makes more sense to analyze it another way. I would say "age" is a noun modified by the determiner "your" to form the phrase "your age"; this in turn is modified by the predeterminer "twice" to form the phrase "twice your age". This phrase is linked to the subject "I" by the verb "am".
In context, "twice" means "two times". Ex:
I'm twice your age! I'm 40, I don't have much in common with twenty-year-olds.
Note it doesn't always mean exactly two times, but an approximation. If a parent were upset about their child dating someone older, for example, they would say "He/she's twice your age!" if the other person were somewhere in the range of two times the child's age.
Since twice modifies am (a verb), twice is an adverb.
You could say "I am your age"; adding twice you are altering the meaning of am.