Question

An angle measuring (468n)° is in standard position. For which value of n will the terminal side fall along the negative portion of the x-axis

Answer 1

since 10*468 = 13*360, if we can find all the values of n < 10, then just adding 10 to those values will produce all the possibilities.

Finding n<10 should not take too long.
For example n=1 works, since 468 = 108(mod 360)

Answer 2

n=5