You could just think out that there would have to be only half as many
white balls as red balls, and half of 8 is 4. 

Otherwise,

...A bag contains 8 red balls and some white balls, all of the same size....

There are 8 red balls and N white balls

There are N+8 balls in the bag.

The probability of drawing a red ball is 8 out od N+8 or


The probability of drawing a white ball is N out of N+8 or


...If the probability of drawing at random a white ball from the bag is half
the probability of drawing a red ball,...



Go to https://www.wolframalpha.com/

Type in N/(N+8) = (1/2)(8/(N+8))

Press ENTER

See N = 4, so there are 4 white balls in the bag.

Edwin