Answer:
Amy has 12 5¢ coins
Step-by-step explanation:
Let <em>x</em> represent 20¢ coins and <em>y</em> represent 5¢ coins. 
Amy has four more 20¢ coins than 5¢ coins. Hence: 

And the total value of all her coins is $3.80. Thus: 

This yields a system of equations: 

We can solve by substitution. Substitute the first equation into the first: 

Distribute: 

Combine like terms: 

And divide both sides by 0.25. Hence: 

Thus, Amy has 12 5¢ coins. 
Using the first equation: 

Substitute: 

Thus, Amy has 16 20¢ coins. 
In conclusion, Amy has 12 5¢ coins and 16 20¢ coins.