Let the number of miles she biked last week be represented by x.
The number of miles Clara wants to bike this week is 2x - 20.
Since Clara wants to bike 112 miles this week, we can set up the equation: 2x - 20 = 112.
Adding 20 to both sides, we get: 2x = 132.
Dividing both sides by 2, we find that x = 66.
Therefore, Clara biked 66 miles last week.