Describe the error in the work, then find the correct product:

\[
\frac{8}{12} \times 6 = \frac{8 \times 1}{12 \times 6} = \frac{8 \times 1}{72} = \frac{8}{72}
\]

Error: The initial step incorrectly distributes multiplication across fractions and integers. The operation should be:

\[
\frac{8}{12} \times 6 = \frac{8 \times 6}{12} = \frac{48}{12} = 4
\]

Correct Product: 4

The error was multiplying the integer by the reciprocal of the fraction instead of the fraction itself. Upon simplifying the fraction and correctly multiplying it by the integer 6, the correct product is found to be 4.

Explanation:

The error in the work is in the multiplication of fractions and integers.

Specifically, the student incorrectly turned the integer 6 into a fraction 1/12 and then multiplied 8 by 1/72, which is not the correct approach to multiplying fractions and integers together.

To find the correct product, one should multiply the whole number 6 by the fraction 8/12 directly.

Let's correct this step by step:

Simplify the fraction 8/12 by dividing both numerator and denominator by their greatest common divisor which is 4. This gives us 2/3.
Now multiply 2/3 by 6. This is the same as multiplying 2 by 6 and then dividing by 3.
The product of 2 and 6 is 12.
Finally, divide 12 by 3 to get the correct answer which is 4.

Therefore, the correct product is 4.