Figure 1 represents a segment of DNA. Radiation can damage the nucleotides in a DNA molecule. To repair some types of damage, a single nucleotide can be removed from a DNA molecule
and replaced with an undamaged nucleotide. Which of the four labeled bonds in Figure 1 could be broken to remove and replace the cytosine nucleotide without affecting the biological
information coded in the DNA molecule?

This question is incomplete. However, what is described in this question is a method of DNA damage repair mechanism. The method described is called base excision repair. Generally, glycosylases play important roles in base excision repair (as they detect and remove these damaged bases).

One thing that can be considered while identifying the bond to be broken is the codon that will be formed after the removal of base. If this codon (a three base sequence) will still produce the same protein as when a normal cytosine was present.

NOTE: During this base excision repair, a glycosylase will detect and remove the damaged cytosine. Once removed, the remaining nucleotide backbone (of the removed cytosine) is also removed and the gap is filled and sealed by other enzymes in this repair mechanism.