Length cannot be measured by

The correct option is debye.

To determine which unit cannot be used to measure length, let us examine each option in detail:

1. Fermi:
A fermi (also referred to as a femtometer) is a unit of length used predominantly in nuclear physics to measure the diameter of atomic nuclei and subatomic particles.
$1fermi={10}^{-15}m$

2. Micron:
A micron (or micrometer) is a metric unit of length commonly used to measure cell sizes, bacterial dimensions, and infrared radiation wavelengths.
$1micron={10}^{-6}m$

3. Light year:
A light year is a unit of astronomical distance, representing the path length that light travels in a vacuum in one Earth year.
$1light\; year\approx 9.46\times {10}^{15}m$

4. Debye:
A debye is a physical unit used to measure the electric dipole moment of molecules. It is defined in terms of charge multiplied by distance (Coulomb-meter in SI units), rather than a pure measurement of length.
$1debye\approx 3.33564\times {10}^{-30}C·m$

Consequently, the debye is the only unit listed that is not a measure of length.