The metal which produces hydrogen gas on reaction with dilute hydrochloric acid as well as sodium hydroxide solution is:

Oxides known as amphoteric oxides react as both an acid and a base. Numerous metals, including lead, beryllium, copper, zinc, aluminum, tin, and aluminum, generate amphoteric oxides or hydroxides. Amphoteric describes aluminum oxide. It reacts both as an acid and a basic. The solid lattice holds the oxide ions too tightly for them to interact with the water.
Because aluminum oxide contains oxide ions, it responds to acids in a similar manner to how sodium or magnesium oxides do.
It functions both as an acid and a base with the base, neutralizing the other and resulting in salt.

As the given metal is reacting with both acid and base, that means the metal is amphoteric in nature.

Aluminum reacts with both hydrochloric acid ($\mathrm{HCl}$) and sodium hydroxide ($\mathrm{NaOH}$) to produce hydrogen gas.
Also, the formula is-

$$\begin{gathered} 2\mathrm{Al} \left(\mathrm{s}\right) + 6\mathrm{HCl} \left(\mathrm{aq}\right) \to 3{\mathrm{H}}_2 \left(\mathrm{g}\right) + 2{\mathrm{AlCl}}_3 \left(\mathrm{aq}\right) \\ 2\mathrm{Al} \left(\mathrm{s}\right) + 2\mathrm{NaOH} \left(\mathrm{aq}\right) + 2{\mathrm{H}}_2\mathrm{O} \left(\mathrm{l}\right) \to 2{\mathrm{NaAlO}}_2+ 3{\mathrm{H}}_2. \end{gathered}$$

Hence, the correct option is C.