The expected values are 54 prefer X, 6 don't.
For the chi-square test, you need to calculate the sum of the squared differences between the observed values minus the expected value, divided by the expected value. Since the claim is 9 out of 10, we should have 0.9 * 60 = 54 doctors prefer brand X and the remaining 60-54 = 6 not preferring brand X.