The correct answer is C. intends, visiting.
A. likes is incorrect because it does not express a strong enough intention to learn German.
B. wants is incorrect because it does not express a specific plan to learn German.
D. tries is incorrect because it does not express a commitment to learning German.
E. knows is incorrect because it does not express a desire to learn German.
The sentence “She intends to learn basic German as she will be visiting Germany next month” expresses the idea that the woman has a strong intention to learn German in order to be able to communicate while she is in Germany. This is a more specific and committed goal than simply liking or wanting to learn German. The woman is also expressing a desire to learn German, which is not evident in the other options.