You can obtain the answer __________ adding.

(a) by.

BY expresses the MEANS or METHOD of doing something, and it is followed by the -ing form: by adding, by walking, by asking.

The pattern to learn: BY + gerund answers the question "how?". You can obtain the answer BY ADDING; he succeeded BY WORKING hard; she travelled BY walking.

Contrast it with WITH, which expresses the INSTRUMENT rather than the method — he wrote WITH a pen, he opened it WITH a key. The distinction between by (how) and with (using what) is examined regularly.

None of the other three prepositions can be followed by a gerund in this construction.

by.