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Hint: Determine the largest four-digit and the smallest four-digit number formed by the digits 6, 1, 2 and 4. Then, multiply them to obtain the answer. Try to figure it out by deciding which digit should be there in a thousand, hundred, tenth and unit place so that the four digit number will be the largest or the smallest number.

Complete step-by-step answer:

To obtain the largest number from the given digits, we need to arrange the numbers in descending order such that the largest digit comes as the first number in the left and the smallest number is in the rightmost digit.

The largest digit is 6, followed by 4, followed by 2 and then 1. Hence, the largest number formed by the digits 6, 1, 2, and 4 is 6421.

To obtain the smallest number from the given digits, we need to arrange the numbers in ascending order such that the smallest digit comes at the leftmost digit and the largest digit is in the rightmost digit. If there is zero, then it must be at the second digit to the left, because if zero is at the leftmost digit, then it is no longer a four-digit number.

The smallest number is formed by 1, followed by 2, followed by 4 and then 6. Hence, the smallest number formed by the digits 6, 1, 2 and 4 is 1246.

We, now, find the product of the numbers 6421 and 1246.

\[6421 \times 1246 = 8000566\]

Hence, the answer is 8000566.

Note: If zero is one of the digits, then you must be careful when expressing the smallest four digit number, zero shouldn’t come at the first digit to the left, then the number becomes three digit.

Complete step-by-step answer:

To obtain the largest number from the given digits, we need to arrange the numbers in descending order such that the largest digit comes as the first number in the left and the smallest number is in the rightmost digit.

The largest digit is 6, followed by 4, followed by 2 and then 1. Hence, the largest number formed by the digits 6, 1, 2, and 4 is 6421.

To obtain the smallest number from the given digits, we need to arrange the numbers in ascending order such that the smallest digit comes at the leftmost digit and the largest digit is in the rightmost digit. If there is zero, then it must be at the second digit to the left, because if zero is at the leftmost digit, then it is no longer a four-digit number.

The smallest number is formed by 1, followed by 2, followed by 4 and then 6. Hence, the smallest number formed by the digits 6, 1, 2 and 4 is 1246.

We, now, find the product of the numbers 6421 and 1246.

\[6421 \times 1246 = 8000566\]

Hence, the answer is 8000566.

Note: If zero is one of the digits, then you must be careful when expressing the smallest four digit number, zero shouldn’t come at the first digit to the left, then the number becomes three digit.