How would you ask a teacher if you can go to study at the library?
a. ¿poder ir a estudiar a la biblioteca? b. ¿puedo ir a estudiar a la biblioteca? *** c. ¿podo ir estudiar a la biblioteca? d. ¿pudo ir a estudiar a la biblioteca?

The interrogative sentence can I go to study at the library? is written in present with the first oerson in singular yo (I).

Therefore, the right conjugation of the verb poder (can) is (yo) puedo.

The other options are incorrect because:

-poder is the verb can in infinitive and this does not match with the grammar context of the sentence

-podo is the conjugation of the verb podar (to prune or to trim) in present with the first pesron in singular yo (I)

pudo is the the conjugation of the verb poder (can) in past with the third person in singular.

me gusta (escribir) en mi cuaderno.

this means : i like to write in my notebook

hopefully this will you out