Answer – 3 parts
The garden is divided into 12 parts.
Karen will plant corn on 8/12 of the garden (or 2/3 of the garden, if both the numerator and denominator are divided by 4).
Therefore, the fewest number of parts she can divide her garden into is 3. She will plant corn on 2/3 of the garden and the other 1/3 of the garden will not be planted with corn.