Question Question about 見える

I have a question about this verb, the potential form of it to be precise.

In the following sentence:
月が見えますか？
"Can you see the moon?"
The potential form of a verb is when you "can" do something, as in the sentence above. I checked both my dictionary of basic grammar and tae Kim's guide:
Rules for creating potential form

• For ru-verbs: Replace the 「る」 with 「られる」.
  Example: 見る → 見られる
• For u-verbs: Change the last character from a / u / vowel sound to the equivalent / e / vowel sound and add 「る」.
  Example: 遊ぶ → 遊べ → 遊べる
• Exceptions:
  1. 「する」 becomes 「できる」
  2. 「くる」 becomes 「こられる」

※Remember that all potential verbs become ru-verbs.

「見る」is a -ru verb. In the example above: 見られる。
How come in my sample sentence it's not the case. I don't understand.

見える is a special verb that work as the potential form of 見る. Incidentally, 見られる also can work as the potential form, and 見える and 見られる are used in different situations. For instance, 見える can be potential when really seeing the object. This is why 見える is used in your example.

Incidentally, 聞こえる also works as the potential form of 聞く other than 聞ける, similar to 見える vs. 見られる.