There is no definitive answer to this question as it depends on how you measure mountains. For example, if you measure by height then Mauna Kea on Earth would be the tallest mountain. However, if you measure by mass then Olympus Mons on Mars would be the largest mountain.
Mauna Kea is a dormant volcano in Hawaii and stands at 10,203 m (33,476 ft) above sea level. However, when measuring from its base underwater to its peak, Mauna Kea is actually taller than Mount Everest at 10,000 m (32,808 ft). This makes Mauna Kea the tallest mountain in the solar system when measured from base to peak.
Olympus Mons is a shield volcano on Mars and is currently the largest known mountain in the solar system. It stands at 21 km (13 mi) high and has a diameter of 600 km (370 mi). Olympus Mons is so large that it can be seen from space with the naked eye.