What is the four most frequently spoken branches of indo-european?

There's a slight misunderstanding in the question. "Branches" of Indo-European refer to major families of languages, not individual languages. So, there are not "four most frequently spoken branches" but rather four most spoken Indo-European language families.

Here they are, along with estimates of their total speakers:

1. Indo-Aryan (1.6 billion speakers): This branch includes languages like Hindi, Urdu, Bengali, Marathi, Punjabi, Gujarati, and many others spoken throughout the Indian subcontinent.

2. Indo-Iranian (1.5 billion speakers): This is a broader branch encompassing Indo-Aryan as well as Iranian languages, including Persian, Pashto, Kurdish, and others.

3. Romance (900 million speakers): This branch comprises languages descended from Latin, such as Spanish, Portuguese, French, Italian, Romanian, and Catalan.

4. Germanic (600 million speakers): Includes languages like English, German, Dutch, Swedish, Norwegian, Danish, and Icelandic.

It's important to note that these numbers are estimates and can vary depending on the source and methodology used. Also, the number of speakers of a branch can change over time due to factors like migration, language shift, and political changes.