Which of the following acid does not react with metals ?

The correct option is C Carbonic acid
Carbonic acid because it is a weak acid and does not dissociate completely in hydrogen ion in aqueous solution where are sulphuric acid, phosphoric acid, and nitric acid are a strong acid. They dissociate completely in aqueous solution form hydrogen ions and radicles. These radicals react with metal to form stable compounds.

For example:

$6Na+2H_{3}P{O}_4\to 2N{a}_{3}P{O}_4+3H_2$

$2Na+H_{2}S{O}_4\to N{a}_{2}S{O}_4+H_2$

$2Na+2HN{O}_3\to 2NaN{O}_3+H_2$

$Na+H_{2}C{O}_3\to NoReaction$