Degrees of freedom refer to the number of independent displacements or rotations that a system can undergo. In the case of a rigid block foundation, the degrees of freedom can be determined by considering the possible translational and rotational movements of the block.

Translational Degrees of Freedom:
A rigid block foundation can move in three orthogonal directions (x, y, and z) in space. Each direction represents a translational degree of freedom. Therefore, there are three translational degrees of freedom associated with a rigid block foundation.

Rotational Degrees of Freedom:
A rigid block foundation can also undergo rotations about three orthogonal axes (roll, pitch, and yaw). These rotations are associated with the rotational degrees of freedom.

Explanation of options:
a) 2: This option is incorrect because it implies that the block foundation has only two degrees of freedom, which does not account for all possible translational and rotational movements.
b) 3: This option is also incorrect because it only considers the translational degrees of freedom and neglects the rotational degrees of freedom.
c) 4: This option is incorrect as well because it does not account for all the translational and rotational degrees of freedom.

Correct answer:
d) 6: This option is correct because it accounts for all possible translational and rotational degrees of freedom. A rigid block foundation has three translational degrees of freedom (x, y, and z) and three rotational degrees of freedom (roll, pitch, and yaw), resulting in a total of six degrees of freedom.

Summary:
A rigid block foundation has six degrees of freedom, including three translational degrees of freedom and three rotational degrees of freedom. These degrees of freedom represent the independent displacements and rotations that the block can undergo.