Introduction:
In structural engineering, the concept of indeterminacy refers to the number of unknown forces or displacements in a structure. A structure is said to be determinate if all its internal forces and displacements can be completely determined using the equations of equilibrium and compatibility. On the other hand, a structure is said to be indeterminate if there are more unknowns than the available equations.

Degrees of Indeterminacy:
Degrees of indeterminacy (DOF) is a measure of the level of indeterminacy in a structure. It represents the number of additional equations or conditions needed to determine the unknown forces or displacements. A structure with two degrees of indeterminacy means that there are two unknowns that cannot be determined by the equations of equilibrium alone.

Plastic Hinges:
Plastic hinges are formed in structural members when they undergo plastic deformation. Plastic deformation occurs when a material exceeds its elastic limit and undergoes permanent deformation. Plastic hinges are formed at locations where the bending moment exceeds the plastic moment capacity of the member.

Analysis:
To understand the relationship between the degrees of indeterminacy and the number of plastic hinges at complete collapse, we need to consider the following points:

1. Plastic hinges form at locations where the bending moment exceeds the plastic moment capacity. Therefore, the number of plastic hinges is directly related to the number of locations in the structure where the bending moment reaches or exceeds the plastic moment capacity.

2. Indeterminate structures have internal redundancy, which allows for redistribution of forces. This redistribution of forces can result in multiple locations where the bending moment exceeds the plastic moment capacity, leading to the formation of plastic hinges.

Conclusion:
Based on the above analysis, the correct answer to the question is option 'D' - 3 plastic hinges. Since the structure has two degrees of indeterminacy, it implies that there are two unknowns that cannot be determined by equilibrium alone. This internal redundancy allows for the redistribution of forces, resulting in multiple locations where the bending moment exceeds the plastic moment capacity. Consequently, three plastic hinges would be formed at complete collapse.