Does the president's cabinet coin money?

Answer 1

Yes. The U.S. Mint coins money and the U.S. Mint has, since its creation in the 1790s, been under the control of the Secretary of the Treasury, which is a cabinet member.

and

No. Congress coins money under Article 1, Section 8, Clause 5. It only delegates the physical job to the US Mint in much the same way that Congress uses the executive branch to enforce laws. When Congress authorizes issuance of new currency, it does not have printing presses in the basement of the Capitol Building to create new dollar bills. The physical job is done by the US Mint; but the Mint cannot coin any money at all unless Congress authorizes it. Saying the "president's cabinet" coins money is inaccurate even though true in a way. The "Cabinet" is the group of secretaries that head the various departments of the executive branch. That group does not coin money, even though the US Mint is within the Secretary of the Treasury's department, which is in the Cabinet.

Both s can be seen as right and wrong depending on how one interprets the question.