Final answer:
The standing committee in the House of Representatives that provides special rules for debating bills is the House Committee on Rules.
Step-by-step explanation:
The standing committee in the House of Representatives that provides special rules under which a bill can be debated, amended, and considered is the House Committee on Rules. This committee establishes the rules of debate, such as time limits and limits on the number and type of amendments. Before a bill reaches the House floor, it must go through this committee to determine the procedures for its consideration.