According to the preamble, why was the constitution written? to provide power to the states to give power to the federal government to provide a common defense

From those choices, the correct answer is:  to provide a common defense.

"A common defense" is just one of several purposes stated in the Preamble.  The Preamble to the US Constitution says:  "We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America."

Incidentally, the term "preamble" stems from the Latin compound word "praeambulus" (prae + ambulus), meaning "walking before" or "going before."  So a "preamble" is an introductory statement to something, going before the main content of the document itself.

uncle sam would be tossing and turning in his grave : *)