How can there be inflation if the level of demand is falling?
When I graph on the aggregate demand-aggregated supply curve the demand falling, it shows a new equilibrium with a lower price, and inflation means higher price. My problem specifically says they are forcasting the inflation of the next year, but the economic problem is that consumer confidence has fallen and consumer spending is decreasing.
If we move from equilibrium a to b, thats a decrease in price. How is that inflation?
The problem that you are having here is that you are only thinking about aggregate demand when you are making your graph. You are correct to say that a decrease in aggregate demand will lead to a drop in the price level, but that is only true if the aggregate supply curve stays where it is.
It is also possible for inflation to be caused by a change in aggregate supply. This sort of inflation is called “cost-push inflation” whereas the kind that is driven by rising aggregate demand is called “demand-pull inflation.” Cost-push inflation happens (in terms of a graph) when the aggregate supply curve drops (moves farther to the left). This can cause the phenomenon that you describe in your question. If the AS curve moves to the left and the AD curve stays where it is, you get people buying fewer things. You also get a higher price level.
Cost-push inflation comes about when the prices of resources climb rapidly. A good example of this is what happens when oil prices jump. This reduces aggregate supply and can lead to inflation even when people are buying less.