The correct answer for the question is option 1, Bhadravahu.

Option 2, Adinatha, is incorrect. Adinatha, who is also known as Adinath or Rishabhanatha, is considered to be the first Tirthankara (spiritual teacher) in Jainism. While he is an important figure in Jainism, he is not credited with the spread of Jainism specifically in Karnataka.

Option 3, Parsvanatha, is also incorrect. Parsvanatha is the twenty-third Tirthankara in Jainism, and he is believed to have lived around 250 years before Mahavira. While he played a significant role in the development of Jainism, he is not credited with the spread of Jainism in Karnataka.

Option 4, Mahavira, is also incorrect. Mahavira is the twenty-fourth and last Tirthankara in Jainism. He is considered to be a reformer and reviver of Jainism, but he is not specifically credited with the spread of Jainism in Karnataka.

Therefore, based on the options provided, the correct answer is Bhadravahu, who is credited with the spread of Jainism in Karnataka.