If C is hybridized sp, that means that there are two p orbitals unhybridized. The two sp orbitals overlap along the bond axis between the nuclei to for the sigma bond. Then the first two p orbitals from each atom overlap top and bottom (kind of like giving ahigh-five and a low five) to form one pi bond. Then the second two p orbitals from each overlap side-to-side, forming the second pi bond.
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