Translation:It is neither near nor far.
と is used like "plus". It means "x and y" when listing multiple things/people/places. E.g. ジョンとマリア ("John and Maria"). も is used like "also". It means "both x and y" when used with a positive verb, and "neither x nor y" when used with a negative verb. E.g. ちかくもとおくもない (literally "both 'not near' and 'not far' " -or in other words- "neither near nor far")
It's probably confusing things to call it the adverb form when it's being used as the negative, since we don't use adverbs like that in English. Easier to think of 〜くない as the negative suffix of an い-adjective, but the く and the ない aren't really tied together, so you can use the same ない for both.
It's a little like in English if you reused the same "anti-" for two different things:
"Do you like cats, or do you like dogs?" "Neither! I'm anti-cats AND dogs!"
they shouldn't teach it like this. better would be: い-adjectives end in い, am i rite, and when you modify a noun with them u use them with the い, wo we've got as an example: ビルは高い (the building is high), or 高いビル (a high building). now, sometimes u gotta cojugate the adjective, like when u want to say a building isnt high but without saying its low. there u replace the い with the くない (い-adj ONLY) to make it negative, so going back to the building: ビルは高くない (the building is not high), or 高くないビル (the building that is not high). u can also make them past by replacing the い with かった for both cases, so 高かったビル (the building that was high), and 高くなかったビル (the building that was not high.
by the way, ビル means building i think?
So, let me get this straight:
In English we have a set expression:
Both A and B ... ("double positive")
In Japanese the same expression would be:
A も B も
Now, for the inverse, "double negative" we have:
English: Neither A nor B ...
Japanese: A も B も ない ...