The octahedral complex of a metal ion $$M^{3+}$$ with four monodentate ligands $$L_1$$, $$L_2$$, $$L_3$$ and $$L_4$$ absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four ligands is:

In an octahedral complex the presence of a ligand produces a splitting of the metal-ion $$d$$-orbitals. The magnitude of this splitting is denoted by $$\Delta_o$$ (crystal-field splitting energy). A stronger ligand produces a larger $$\Delta_o$$, whereas a weaker ligand produces a smaller $$\Delta_o$$.

When an electron is promoted from the lower $$t_{2g}$$ set to the higher $$e_g$$ set, the energy absorbed by the complex is exactly $$\Delta_o$$. The same energy is related to the wavelength $$\lambda$$ of the absorbed light by the well-known relation of photon energy

$$E = h\nu = \frac{hc}{\lambda},$$

where $$h$$ is Planck’s constant, $$\nu$$ is the frequency of light and $$c$$ is the speed of light.

Substituting $$E = \Delta_o$$, we obtain

$$\Delta_o = \frac{hc}{\lambda}.$$

From this expression we see that $$\Delta_o$$ is inversely proportional to $$\lambda$$:

$$\Delta_o \propto \frac{1}{\lambda}.$$

Hence, a shorter (smaller) wavelength corresponds to a larger splitting energy and therefore to a stronger ligand, while a longer (larger) wavelength corresponds to a weaker ligand.

The question tells us that the four ligands absorb light in the regions shown below (the approximate central wavelengths are given for clarity):

$$L_1 : \text{red} \; (\lambda \approx 700\,\text{nm})$$
$$L_2 : \text{green} \; (\lambda \approx 530\,\text{nm})$$
$$L_3 : \text{yellow} \; (\lambda \approx 580\,\text{nm})$$
$$L_4 : \text{blue} \; (\lambda \approx 450\,\text{nm})$$

Arranging these wavelengths from the longest to the shortest (and hence from the weakest to the strongest ligand), we have

$$700\,\text{nm} \;(\text{red}) \; > \; 580\,\text{nm} \;(\text{yellow}) \; > \; 530\,\text{nm} \;(\text{green}) \; > \; 450\,\text{nm} \;(\text{blue}).$$

Translating this wavelength order back to the ligands:

$$L_1 \;(\text{red}) \; < \; L_3 \;(\text{yellow}) \; < \; L_2 \;(\text{green}) \; < \; L_4 \;(\text{blue}).$$

Thus the increasing order of ligand strength (from the weakest to the strongest) is

$$L_1 \lt L_3 \lt L_2 \lt L_4.$$

Hence, the correct answer is Option B.