[semolinapudding]

There is a nice illustration of a 2-sphere wrapped twice around another 2-sphere on the Wikipedia article for the homotopy groups of spheres [0].

Now, there are many ways of proving that there is only one way (up to homotopy) of wrapping a 2-sphere n times around another 2-sphere, but all of them are fairly involved. The simplest proof comes from an analysis of the Hopf fibration, which roughly describes a relation between the 1-sphere, the 2-sphere and the 3-sphere [1]. Other than this, it follows from the theory of degrees for continuous mappings, or from the Freudenthal suspension theorem and some basic homological computations.

[0] https://en.wikipedia.org/wiki/Homotopy_groups_of_spheres#/me...

[1] https://en.wikipedia.org/wiki/Hopf_fibration