1. Interpret ppm for dissolved oxygen

For dilute solutions in this context, $5.8\,\text{ppm}$ means: $5.8\,\text{mg of } O_2 \text{ per } 1\,\text{kg of solution}$

So, in $1000\,\text{g}$ of sea water, mass of dissolved $O_2$ is $5.8\times 10^{-3}\,\text{g}$

2. Find moles of dissolved oxygen

Molar mass of $O_2 = 32\,\text{g mol}^{-1}$

Hence, $n(O_2)=\frac{5.8\times 10^{-3}}{32}=1.8125\times 10^{-4}\,\text{mol}$

3. Find mass of NaCl in 1 kg of sea water

Sea water is $6\,\text{M}$ NaCl and density is $2\,\text{g mL}^{-1}$.

So, mass of $1\,\text{L}$ solution is $1000\,\text{mL}\times 2\,\text{g mL}^{-1}=2000\,\text{g}$

Since it is $6\,\text{M}$, in $1\,\text{L}$ solution moles of NaCl are $6$.

Mass of NaCl in $1\,\text{L}$ solution: $6\times 58.5=351\,\text{g}$

Therefore, in $2000\,\text{g}$ solution, NaCl mass $=351\,\text{g}$.

So in $1000\,\text{g}$ solution, NaCl mass is $\frac{351}{2}=175.5\,\text{g}$

4. Find mass of solvent (water) in 1 kg solution

Mass of solvent $=1000-175.5=824.5\,\text{g}=0.8245\,\text{kg}$

5. Calculate molality of dissolved oxygen

Molality, $m=\frac{\text{moles of solute}}{\text{kg of solvent}}$

Thus, $m=\frac{1.8125\times 10^{-4}}{0.8245}=2.20\times 10^{-4}\,m$

So, $x\times 10^{-4} = 2.20\times 10^{-4}$

Hence, $x\approx 2$

6. Final answer

Nearest integer value of $x$ is: $\boxed{2}$

7. Comparison with stored answer

Stored correct answer = $2$.

Our derived answer matches the stored answer.