You can think 四本足 is a fixed noun (or no-adjective) meaning "quadrupedal", or you can think of 本足 as a counter on its own. Either way, it has little to do with how you usually count the number of apples or pencils in an ordinary sentence. To express "Dogs have four legs" (rather than "Dogs are quadrupedal") as an ordinary sentence, you can say either of these:
- 犬には足が4本ある。
- 犬には4本の足がある。
(To be precise, I think 四本足 is not as technical-sounding as "quadrupedal", but it's still a fixed compound.)
There are a few fixed terms that look like 四本足, including 一本槍, 二人羽織, 三羽烏 and 五人囃子. But these are essentially to be memorized as compound words, and they are not common enough to be rightfully called a "3rd pattern".