Final answer:
The president does not have the power to vote to impeach a government official; this is a Congressional power. The president can veto a budget, propose a budget, and establish foreign policy.
Step-by-step explanation:
The correct answer is b. vote to impeach a government official. The president does not have the power to vote to impeach; this power resides with the House of Representatives, which can impeach federal officials, including the president. The Senate then conducts the trial for impeachment. The other options listed are indeed powers of the president: they can veto a budget, propose a budget to Congress, and establish foreign policy as part of their executive powers.
Explanation: The presidential power to veto a budget (a) is a check on legislative power, allowing the president to refuse to sign a bill into law. However, Congress can override a presidential veto with a two-thirds majority in both the House and Senate. Proposing a budget (c) is part of the president's administrative responsibilities, as they often set the policy agenda and then present a budget to fund these priorities. Establishing foreign policy (d) is a part of the executive’s responsibility, though it often requires cooperation with Congress, which holds the power of the purse and can approve or deny funding for foreign policy endeavors.