Final answer:
To find the multiples of 6 between 50 and 100 that are also multiples of 8, we must look for multiples of 48 within this range. The only number that fits these criteria is 96, making option c) the correct answer.
Step-by-step explanation:
The question asks to find the multiples of 6 between 50 and 100 that are also multiples of 8. To solve this, we need to find a common multiple of both 6 and 8 that lies within the specified range. Since the least common multiple (LCM) of 6 and 8 is 24, we can start by finding the multiples of 24 and then check which ones are greater than 50 and less than 100. However, to satisfy both conditions, we need to find a number which is a multiple of the LCM of 6 and 8, so in this case, it should be a multiple of 48 (since 24 * 2 = 48, which is the LCM of 6 and 8).
The multiples of 48 between 50 and 100 are 48, 96. However, only 96 is greater than 50. Therefore, the only number from the given options (54, 72, 96, 84) that is a multiple of 6, also a multiple of 8, and falls between 50 and 100 is option c) 96.