what is the place the sun shines for 6 months and sets for 6 months?

Answer 1

You're being incorrect in stating your question.

The sun "shines" continuously for 24-hour periods in all locations north of the Arctic Circle (66 degrees north latitude) and south of the Antarctic Circle (66 degrees south latitude). The farther toward the poles you travel, the longer the period of continuous sunshine. For example ... in Fort Simpson (NWT, Canada) the "long days" are only around for perhaps three months. This is slightly above the magic 66 N latitude condition.

However, the second portion of your question - taking it exactly as it's worded - won't give you the answer you're seeking. The sun "sets" every day, at every place on the globe. It's not always visible (particularly in the polar extremities), but it DOES set.

Answer 2

Alaska

Answer 3

at the north and south poles