Since [tex]x[/tex] is simultaneously a multiple of 4, 6, and 8, it must be also be a multiple of the least common multiple of the three, which would be 24. So any [tex]x=24n[/tex], where [tex]n[/tex] is an integer, such that [tex]67\le x\le113[/tex] will belong to the desired set of numbers.
The number of positive multiples of 24 less than or equal to 113 is [tex]\left\lfloor\dfrac{113}{24}\right\rfloor=4[/tex], while the number of positive multiples of 24 less than or equal to 67 is [tex]\left\lfloor\dfrac{67}{24}\right\rfloor=2[/tex], so there are [tex]4-2=2[/tex] numbers that are each multiples of 4, 6, and 8, and fall between 67 and 113. These numbers are 72 and 96.
