Step 1: Understand the concept
The conductivity of an electrolyte solution depends on the number of free ions and their mobility. At equal molarity, the substance that ionises most gives the highest conductivity.
Step 2: Check HCl
HCl is a strong acid and ionises completely into \(\text{H}^+\) and \(\text{Cl}^-\). The \(\text{H}^+\) ion also has an exceptionally high mobility, so HCl conducts best.
Step 3: Check the others
\(\text{CH}_3\text{COOH}\) is a weak acid and ionises only slightly. \(\text{NH}_4\text{OH}\) is a weak base and also ionises slightly. \(\text{C}_6\text{H}_{12}\text{O}_6\) (glucose) is a non-electrolyte and gives no ions at all.
Step 4: Conclusion
Complete ionisation puts HCl far ahead of the weak electrolytes and the non-electrolyte.
Final Answer:
HCl is a strong electrolyte, so it conducts best. This is option (C).
\[ \boxed{\text{(C) }\text{HCl}} \]