Introduction:
The emission spectrum of hydrogen consists of a series of lines in the visible region. These lines correspond to transitions between different energy levels in the hydrogen atom. Each line in the spectrum corresponds to a specific transition. In this case, we are interested in determining the transition that gives rise to the third line from the red end of the spectrum.

Explanation:
To understand which transition corresponds to the third line from the red end, we need to examine the energy levels involved in each transition. The energy levels in the hydrogen atom are labeled with principal quantum numbers (n). The lower energy level is represented by the initial quantum number (ni), and the higher energy level is represented by the final quantum number (nf).

Transition (a): 3--->2
In this transition, the electron moves from the third energy level (n=3) to the second energy level (n=2). The energy difference between these levels corresponds to the emission of a photon in the visible region. However, this transition does not give rise to the third line from the red end of the spectrum.

Transition (b): 6--->2
In this transition, the electron moves from the sixth energy level (n=6) to the second energy level (n=2). The energy difference between these levels corresponds to the emission of a photon in the visible region. However, this transition does not give rise to the third line from the red end of the spectrum.

Transition (c): 4--->2
In this transition, the electron moves from the fourth energy level (n=4) to the second energy level (n=2). The energy difference between these levels corresponds to the emission of a photon in the visible region. This transition gives rise to the third line from the red end of the spectrum.

Transition (d): 5--->2
In this transition, the electron moves from the fifth energy level (n=5) to the second energy level (n=2). The energy difference between these levels corresponds to the emission of a photon in the visible region. However, this transition does not give rise to the third line from the red end of the spectrum.

Conclusion:
Based on the analysis, we can conclude that the transition (c) from the 4th energy level to the 2nd energy level corresponds to the third line from the red end of the visible spectrum.