Why did the United States bombed Libya, Iraq, Syria, Yemen?

Those were Obama's messes

The United States did not take an active role in the Arab Spring civil rebellion in Libya beyond providing off-shore missile cover for the UN-imposed "No Fly Zones" flights of France and the United Arab League (UAL). Once the dictator Muammar Gaddafi called upon his military to "go door to door" to kill any would-be protestors and their families, the Libyan people appealed to the United Nations for help, so the UN voted to set up "No Fly Zones" in Libya for the military as a way to protect the rebels. Then-Secretary of State Hillary Clinton thought it would be unwise for the U.S. to lead such an operation, so then-French President Zarkosy agreed to take the lead. All the U.S. did was provide protection for the flights.

The Cheney/Bush illegal 2003 invasion of a sleeping Iraq turned the U.S. into a terrorist nation, and the subsequent Cheney-ordered TORTURE of Iraqi men (Sunnis, mostly) means that our nation committed crimes against humanity for which the Bush/Cheney administration should be held accountable before the World Court at The Hague. Oilman Cheney wanted to get himself an oil-rich foothold in the Middle East, picking Saddam Hussein because Saddam had been cultivated while Cheney was head of the CIA to be our CIA DUPE and our "best buddy," setting him up. The lawless Bush/Cheney White House kept on retainer a right-wing PR firm named HILL & KNOWLTON in Washington to falsely paint Saddam Hussein as "a villain" to the American people, a dirty trick ordered by Cheney that was exposed on a "60 Minutes" segment during the Bush/Quayle years---all a set-up for later on.

The U.S.-led military strikes in Syria were done on ISIL (Islamic State in Iraq and the Levant) strongholds with the tacit (unspoken) permission of Bashar al-Assad, the Syrian dictator. Diplomatically gifted President Obama was able to forge a huge coalition of other nations to help go after ISIL and to share the costs for doing so. The U.S. personnel currently in Syria are a contingency force for on-ground intelligence and to train in special forces tactics so that the Syrians can take over their own defense.

To kill the enemy. A 500-lb JDAM dropped on their towel head works extremely well.

To remove the anti-American governments in those places. A lot of people will just say "oil" and leave it at that, and while oil did play a role in Iraq, it's a lot more complicated and bigger than just the oil industry.

Gadhafi was removed for example for wanting to put Africa on the gold standard, which would have destroyed Western economies.

Im not sure you have that right or in order.