Look at it this way, Let Y be a normal random variable such that, Y = X - 15, now Y~N(0,4)
And you want P(|y|<w); This means that the only area you are not looking for is 1-0.9 = 0.1; but since the normal is symmetric you have 0.05 of that on each side.
So now look up the Z value for a probability of 0.05 and plug it in to the standardization equation: Z = (w - 0)/2. This obtains the answer.