why can't the government just print more mney?

It is faster and easier to print a check .

Because if you have more of what represents currency, then each one becomes less valuable. That's called inflation. For instance, lets say that there are only 10 $1 bills in existence. If something costs $1, then that's a LOT, because it's 10% of ALL the dollar bills. But if you then print up another Billion Dollar bills, then that piece of currency is only 1 in a billion, and not worth as much.

When the government prints "more" money the value of all money in circulation decreases, producing inflation in prices of goods and services. 

The government can print more money.  Any government with its own currency can just print as much money as they want.  But printing more money causes inflation.  The more dollars there are in circulation the less each dollar is worth.  So printing more money will increase prices and decrease purchasing power.  It will also devastate saving since all of that saved money will be worth less.

I heard something like twenty trillion dollars were printed this year. Put your money in silver, it's going to go through the roof. Already rose by 50% or more. 

That wouldn't work because of hyperinflation.