These transitions correspond to the Balmer series (transitions to $n_1=2$) in the hydrogen spectrum . The wavelength ($\lambda$) is inversely proportional to the energy difference ($\Delta E$) of the transition ($\Delta E = hc/\lambda$).

1. Transition A ($n_2=3 \to n_1=2$): This represents the smallest energy gap in the series, corresponding to the longest wavelength (Red line, $H_\alpha$). Matches III (656.3 nm).
2. Transition D ($n_2=6 \to n_1=2$): This represents the largest energy gap among the given options, corresponding to the shortest wavelength (Violet line, $H_\delta$). Matches I (410.2 nm).
3. Transition B ($n_2=4 \to n_1=2$): Intermediate energy ($H_\beta$). Matches IV (486.1 nm).
4. Transition C ($n_2=5 \to n_1=2$): Intermediate energy ($H_\gamma$). Matches II (434.1 nm).

Therefore, the correct matching is A-III, B-IV, C-II, D-I.