このコルクの栓はどうしてもぬけない。

this (something or someone close to the speaker (including the speaker), or ideas expressed by the speaker)

cork

indicates possessive; nominalizes verbs and adjectives; substitutes for "ga" in subordinate phrases; (at sentence-end, falling tone) indicates a confident conclusion; (at sentence-end) indicates emotional emphasis; (at sentence-end, rising tone) indicates question

stopper; cork; stopcock

topic marker particle; indicates contrast with another option (stated or unstated); adds emphasis

by all means; at any cost; no matter what; after all; in the long run; cravingly; at any rate; surely

to come out; to fall out; to be omitted; to be missing; to escape; to come loose; to fade; to discolour; to wear a hole (e.g. clothes); to leave (e.g. a meeting); to be clear; to be transparent (e.g. of the sky); to be stupid; to be absentminded; to be careless; to be inattentive; to exit (a program loop)