"...To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof."

This clause was used by Secretary of the Treasury Alexander Hamilton to justify
a. establishing the Bank of the United States
b. creating a federal postal system
c. sending troops to end the Whiskey Rebellion
d. imposing an embargo on trade with Great Britain

"Alexander Hamilton used the Elastic Clause to create the first National Bank. People argued that the constitution did not grant the power to create a bank, Hamilton noted that it was required in order to carry out taxation. Another great example of the use of the elastic clause would be the Louisiana Purchase."

The Elastic Clause - Elastic Clause
https://npelasticclause.weebly.com/

The clause you are referring to is a part of Article I, Section 8, Clause 18 of the United States Constitution, commonly known as the "Necessary and Proper Clause" or the "Elastic Clause." This clause grants Congress the authority to make laws that are necessary and proper for carrying out the powers delegated to the federal government.

To determine how the Necessary and Proper Clause was used by Secretary of the Treasury Alexander Hamilton, we need to consider the options given:

a. establishing the Bank of the United States: This is correct. Alexander Hamilton indeed used the Necessary and Proper Clause to justify the establishment of the Bank of the United States. He argued that the creation of a national bank was necessary and proper for Congress to carry out its enumerated powers, such as the power to regulate commerce and collect taxes.

b. creating a federal postal system: While the establishment of a federal postal system falls within Congress's powers to regulate interstate commerce and establish post offices, it is not directly related to the Necessary and Proper Clause. So this option is not directly connected to Hamilton's use of the clause.

c. sending troops to end the Whiskey Rebellion: The ability to send troops to quell domestic rebellions falls within the federal government's power to provide for the common defense and maintain domestic tranquility. However, it is not directly connected to Hamilton's use of the Necessary and Proper Clause.

d. imposing an embargo on trade with Great Britain: The power to impose embargoes on foreign trade is related to Congress's authority to regulate foreign commerce but is not directly connected to Hamilton's use of the Necessary and Proper Clause.

In conclusion, the correct answer is:

a. establishing the Bank of the United States