Now consider the time to begin at 2.3 min, where [H2O2] = 0.50 M. How much time is required to cut the concentration in half again, in this case from 0.50 M to 0.25 M?

2.3 minutes

Explanation:

The half life of any reaction is the amount of time it takes to consume half of the starting material.

The Half life of a reaction is usually constant for that particular material.

From the question it takes 2.3 min to cut the concentration in half to a concentration of 0.5M

How much time it would then take to cut the concentration in half again, in this case from 0.50 M to 0.25 M?

It's still going to take 2.3 minutes which is the half life.