H2O2 is

The oxidation number of oxygen in hydrogen peroxide is -1.Now the oxygen atom can show two stable oxidation states that are -2 and 0.

In acidic condition the oxidation state is transformed from -1 to -2 and formation of water molecule take place so it itself gets reduced and act as strong oxidizing agent for others.

PbS ÷ 4H₂O₂ → PbSO₄ + 4H₂O₂

In basic condition the oxidation state also Converts from -1 to 0 ,it itself gets oxidized but acts as strong reducing agents for others.

H₂O₂ ÷ Ag₂O → Ag + H₂O + O₂

So hydrogen peroxide can act as both oxidizing and reducing agent.

The correct option is ( B) both oxidising and reducing agent