Get pink, blue, red or green

Solution: 474 / 4 =118 r 2 so, pink has a remainder of 1, red has a remainder of 2, and so on. Green is always divisible by four so it divides perfectly so we can call this remainder 0. Therefore the answer is red.

The pattern repeats after every 4 balls. Thus the 4th ball will be green, the 8th will also be green, and every multiple of 4 will be green. Thus 472nd colour will also be green. 473rd colour will be pink. And then the 474th colour will be $\boxed{\color{#D61F06}{\text{red}}}$