President Nixon endorsed Vietnamization because // A) he beleived it would win the war // B) it would bring American troops home...

Of the answer that you give, D is the best.  B is also
somewhat possible, but the fact that it uses the word "immediately" makes it
incorrect.

The main point of the Vietnamization strategy
was to get US troops out of Vietnam.  However, Nixon did not believe that this would be
immediately possible.  Instead, he believed that he would be able to bring the troops
home more quickly.  As the link below
says,

Under
this new policy, American forces would gradually transfer responsibility for Saigon's
defense to the South Vietnamese military, freeing U.S. troops to return
home.

Note the use of the
word "gradually."  This shows that Nixon did not expect immediate
results.

Since B is not correct, D is the best answer
because Nixon did hope that the South Vietnamese government would become stronger and
more stable.