The highlighted atoms have sp2 - sp3 hybridization. The highlighted atoms are carbon and nitrogen as shown.
The structure of Xanthine is shown in the image attached to this answer. The indicated atoms are Carbon and nitrogen as shown. Let us remember that hybridization has to do with the mixing of atomic orbitals to form appropriate hybrid orbitals that are suitable for overlap with orbitals of other atoms.
The highlighted carbon atom is sp2 hybridized because it has a carbon nitrogen double bond while the highlighted nitrogen atom is sp3 hybridized. Therefore, the highlighted atoms have sp2 - sp3 hybridization.
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