Homoleptic octahedral complexes of a metal ion $$M^{3+}$$ with three monodentate ligands $$L_1$$, $$L_2$$ and $$L_3$$ absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is:

For an octahedral complex, the five $$d$$-orbitals split into two groups with an energy gap denoted by $$\Delta_o$$. A transition of an electron from the lower set to the higher set occurs by absorbing a photon whose energy equals this gap.

The energy of a photon is given by the Einstein-Planck relation

$$E \;=\; h\nu \;=\; \dfrac{hc}{\lambda},$$

where $$h$$ is Planck’s constant, $$\nu$$ is the frequency, $$c$$ is the speed of light and $$\lambda$$ is the wavelength of the absorbed light. From the relation $$E \propto \dfrac1\lambda$$ we see that

shorter wavelength $$\;( \text{smaller }\lambda ) \;\Longrightarrow\;$$ higher energy $$E$$,

and conversely, longer wavelength $$\;( \text{larger }\lambda ) \;\Longrightarrow\;$$ lower energy $$E$$.

In ligand field theory a stronger field ligand produces a larger splitting $$\Delta_o$$, so a complex containing a stronger ligand must absorb higher-energy (hence shorter-wavelength) light. Therefore

$$\text{larger }\Delta_o \quad\Longleftrightarrow\quad \text{shorter }\lambda_{\text{absorbed}}\quad\Longleftrightarrow\quad \text{stronger ligand.}$$

The three homoleptic complexes described absorb in the following spectral regions:

$$L_1:\; \text{green} \quad(\lambda \approx 520\text{-}560\ \text{nm})$$
$$L_2:\; \text{blue} \quad(\lambda \approx 450\text{-}495\ \text{nm})$$
$$L_3:\; \text{red} \quad(\lambda \approx 620\text{-}750\ \text{nm})$$

Comparing the wavelengths numerically, we have

$$\lambda_{\text{blue}} \lt \lambda_{\text{green}} \lt \lambda_{\text{red}}.$$

Using $$E = hc/\lambda$$, the corresponding energies and hence ligand strengths follow the reverse order:

$$E_{\text{blue}} \gt E_{\text{green}} \gt E_{\text{red}}$$

$$\Longrightarrow\quad L_2 \;(\text{blue})\; \text{is the strongest field ligand},$$

$$\phantom{\Longrightarrow}\quad L_1 \;(\text{green})\; \text{is of intermediate strength},$$

$$\phantom{\Longrightarrow}\quad L_3 \;(\text{red})\; \text{is the weakest field ligand}.$$

Thus, arranged from the weakest to the strongest ligand, the increasing order is

$$L_3 \;\lt\; L_1 \;\lt\; L_2.$$

This order corresponds to the option written as $$L_2 \gt L_1 \gt L_3$$ when read from left (strongest) to right (weakest), which is Option C in the list given.

Hence, the correct answer is Option C.