Which two incidental motions require a two-thirds vote to carry?

The correct choice highlights two incidental motions that indeed require a two-thirds vote for approval. "Suspend the Rules" is a motion that allows the assembly to temporarily set aside rules to facilitate the current business. Since this could significantly alter the flow of the meeting, a higher threshold is necessary to ensure that the will of the group is clear and that any decision made by this method is broadly supported.

The other motion, "Object to Consideration," likewise requires a two-thirds vote as it seeks to prevent a particular matter from being considered at all. This is a critical procedural step since it helps maintain order in the meeting by allowing members to ensure that not everything proposed reaches discussion.

Both of these motions involve significant procedural implications and therefore necessitate a strong consensus among the members, demonstrated by the requirement for a two-thirds majority. This requirement serves to protect the rights of members and ensures that only motions with substantial support are allowed to interrupt regular proceedings.