Among other themes that are painted are episodes from the Bhagvata Purana, Ramayana, stories of Shiva-Parvati, Durga, Kali and Rasa-Lila of Radha and Krishna. Mithila artists do not like empty spaces. They fill in the entire space decoratively with elements from nature like birds, flowers, animals, fish, snakes, the Sun and the moon, which often have symbolic intent, signifying love, passion, fertility, eternity, well-being and prosperity. Women paint with bamboo twigs to which some cotton swab, rice straw or fibre is attached. In earlier days, they made colour from mineral stones and organic things, such as phalsa and kusum flowers, bilwa leaves, kajal, turmeric, etc.

How do Mithila artists avoid empty spaces in their paintings?

By filling the entire space decoratively with elements from nature

Answer:  By filling the entire space decoratively with elements from nature
The passage mentions that Mithila artists do not like empty spaces and fill the entire space decoratively with elements from nature.
Among other themes that are painted are episodes from the Bhagvata Purana, Ramayana, stories of Shiva-Parvati, Durga, Kali and Rasa-Lila of Radha and Krishna. Mithila artists do not like empty spaces. They fill in the entire space decoratively with elements from nature like birds, flowers, animals, fish, snakes, the Sun and the moon, which often have symbolic intent, signifying love, passion, fertility, eternity, well-being and prosperity. Women paint with bamboo twigs to which some cotton swab, rice straw or fibre is attached. In earlier days, they made colour from mineral stones and organic things, such as phalsa and kusum flowers, bilwa leaves, kajal, turmeric, etc.