The element having the highest binding energy per nucleon among the following is:

${^{16}_{}O}$

The correct answer is Option (4) → ${^{16}_{}O}$

Binding energy per nucleon indicates the stability of a nucleus. It is the total binding energy divided by the number of nucleons. Nuclei with higher binding energy per nucleon are more stable.

For light elements (low atomic number), the binding energy per nucleon increases with mass number. Among the given options:

- $^6\text{Li}$ → 6 nucleons, relatively low binding energy per nucleon

- $^{12}\text{C}$ → 12 nucleons, higher than $^6\text{Li}$

- $^{14}\text{N}$ → 14 nucleons, slightly higher than $^{12}\text{C}$

- $^{16}\text{O}$ → 16 nucleons, the highest among the four options

Thus, $^{16}\text{O}$ has the highest binding energy per nucleon among the listed elements.

Final Answer: $16_O$