I'm guessing that dobler (to double something) means to fold it, which makes practical sense. The problem is that DuoLingo clearly doesn't yet have the ability to selectively show different definitions based on context, because there are many many verbs that are spelled the same as (usually related) nouns, et cetera. Once they figure out a work around this, many problems will be solved.
I looked this up. ''Fuerza'' (strength) is a noun. ''Fuerte'' (strong) is an adjective. Also, even if you translate it using a noun, you would say "You have twice the strength that I have'' (or ''that I do''). You can't ''be'' (your ''you are'' and ''I am'') strength in English.
It actually equals THAN.
Let's break it down. Shall we?
"Eres el doble de fuerte que yo."
Literal translation: *"You are [the] double [of] strength than I."
Eres = You are
el doble = double
de fuerte = (the) strength
que yo = than I/as me
el doble de fuerte = twice as strong (double the strength)
In this case AS = THAN.
I hope that helps. ^_^
Because the phrase has a parallel structure: "You are" "I am" are conjugations of the same verb ("to be"). You can't "do" what someone else "is."
As you'll see from various comments on this particular forum, one of the big debates is whether "I" or "me." is correct here, but no one is debating whether we can use "I am" versus "I do."
Re the "I/me," English grammarians regularly have dust-ups over this. In this sentence, most casual English speakers use "me." The formal way (read "correct" for some) is "I."
Duolingo is inconsistent in its application of formal versus general use: sometimes it is formal only, sometimes it gives us the general usage only and sometimes it allows both. Your job: to outguess Duolingo in these matters, then fight righteously for whatever grammatical side you are on. :)
Though, it's worth noting that im English "do" often be used in such a situation (as something like a shorthand for other verbs): "you have twice as much money as I do", is fine, and in fact (in my dialect at least) more natural than "... as much money as I have".
The problem with your sentence is just that "to be" is (I think) the only verb for which the above (substituting "do" for another verb) doesn't apply. It's the same principle as "do you have?"/"I don't", but "are you?"/"I'm not" (never "I don't" for the verb "to be").