The Short Version
The claim is true. Africa's landmass is crossed by both the Equator (dividing Northern and Southern Hemispheres) and the Prime Meridian (dividing Eastern and Western Hemispheres), placing it in all four hemispheres. This is confirmed by multiple credible geographic sources including WorldAtlas, Royal Museums Greenwich, and others. The East/West division relies on the conventionally chosen Prime Meridian at Greenwich, but this is the universally accepted standard in geography and cartography.