In Year 1 suppose the economy is at potential GDP and that the federal budget deficit equals $100 billion. In Year 2 the federal budget deficit rises to $150 billion, but the cyclically adjusted budget deficit falls to $75 billion

How can the actual budget deficit rise and the cyclically adjusted budget deficit fall?

The rise in the actual budget deficit with a decline in the cyclically adjusted budget deficit indicates that the economy grew less than anticipated in Year 2, perhaps falling into a recession. The decline in the cyclically adjusted budget deficit indicates that the budget deficit would have fallen if the economy had been at potential GDP in Year 2.