The governments of spain and portugal sponsored overseas exploration and expansion in the late 1400s and into the 1500s because they (1) desired spices from the indies (2) owed allegiance to islamic caliphates (3) militarily defeated the ottoman empire (4) lacked access to northern africa

The answer is likely the first one, "desired spices from the Indies". In the mid 15th century after the Ottoman Empire defeated Byzantium, they cut the European spice trade.

The Spanish decided to try and to India by sailing west--accidentally discovering the Americas--and the Portuguese went south around the south of Africa and up to India.