The power of recognition allows the speaker of the house to

To determine who speaks and how long a debate can last.

Explanation:

One of the powerful political office holder in the Legislative arm or branch of government is the Speaker of the House of Representatives. The speaker of the house of Representatives is elected by the members of the house of Representative.

During debate, the speaker has the power to determine who to speak and how long the debate is going to last, such power of the speaker of the house of Representatives is know as the "power of recognition".