"I have a lot of long pencils."
Translation:У меня много длинных карандашей.
"Есть" is emphasizing the existence of an object, rather than a characteristic (such as number). I guess here the fact of interest is not that you have pencils but that you have a lot of them. That said, I wouldn't be confident that "есть" is necessarily wrong here, it's maybe worth reporting just in case.
What I was told by a native Russian speaker is that you only use есть if you are emphasizing the existence of something. As far as I can understand, that means if there are any modifiers that are not inherent properties (e.g. number, adjective) then you shouldn't use есть. In this case, the existence of pencils is implied, and "many" and "long" are simply saying what type of pencils they are. So there should be no "есть". This is my understanding. One example that I saw was I have a good jacket. I answered я меня хорошая куртка, it accepted that but also suggested я меня есть хорошая куртка. My interpretation is that in the first case, you have a jacket and you are saying it is good, in the second case, you are saying you have a "good jacket", as in a jacket used as formal wear or for special occasions.
You can think about the scenario where you go into a store. You wouldn't ask someone working there "Do you have many long pencils?" You would say "Do you have pencils?" and THEN you would ask what type they are.