Question

State programs such as education, transportation, and public safety are implemented by which branch of government?

Answer 1

Well there are three different branches of government: executive, legislative, and judicial. In the simplest sense, the legislative branch makes the laws, the executive branch executes them, and the judicial branch determines if the laws are constitutional (This is a VERY simplified version, each branch is much more complex but we don't need to get into it) These branches exist at both the state and national level.
Based on this, which branch do you think would implement programs in general?

Answer 2

Most state governments are set up very similar to the national government. So the 3 branches idea works with States too. Your looking for the branch that can execute the law. Not just legislate it or adjudicate it.