To subtract 2/3 from 45 1/6, we need to convert the mixed number to an improper fraction.
45 1/6 can be written as (45 * 6 + 1)/6 = 271/6.
Now, we can subtract 2/3 from 271/6.
271/6 - 2/3 = (271 * 3 - 2 * 6)/(6 * 3) = (813 - 12)/18 = 801/18.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 9.
801/18 = (801/9)/(18/9) = 89/2.
So, 45 1/6 - 2/3 is equal to 89/2.