Which of the following types of hybridisation leads to three dimensional geometry of bonds around the carbon atom?

The correct option is sp².

To understand why this option is correct, let us analyze the nature of the hybrid orbitals and the overall bonding environment around the carbon atom:
In ^sp² hybridisation, one s-orbital mixes with two p-orbitals to form three equivalent hybrid orbitals. These three hybrid orbitals lie in a single two-dimensional plane, directed towards the corners of an equilateral triangle with characteristic bond angles of 120°.

However, the carbon atom also retains one unhybridised p-orbital that is oriented perpendicular to this plane. When carbon forms a double bond, this unhybridised p-orbital overlaps sideways with a neighboring p-orbital to establish a π (pi) bond. The electron cloud of this π bond lies concentrated in regions directly above and below the planar σ (sigma) framework. Consequently, the combination of the planar σ bonds and the perpendicular π orbital density creates a three-dimensional spatial distribution of bonds and electron density around the carbon atom.