The LCD is the least common denominator, or the smallest value that is divisible by both 12 and 8. In this case the LCD is 24 because it is the smallest number that 8 and 12 goes into.
Tasha's mistake is in Step 4
she has a negative sign in front of the fraction and she has a negative exponent on the 4 in the denominator
That'd be one third of 1500 muffins, or 500 muffins.
6 bagels, 4 students
6 / 4 = 1 1/2 of a bagel for each student