MPC, or marginal propensity to consume, refers to the willingness to spend money. For instance, if a person were given $100 and they only spend $80 of that, the marginal propensity to consume would be 80/100 = 0.8
If the financial situation requires an increase in aggregate demand, the government can do the same by increasing its expenditure. An increase in government expenditure by X increases the aggregate demand by a value greater than X and the ratio of the two is called the multiplier. The multiplier M = 1/(1 - MPC)
In the given problem, the MPC is equal to 0.6. In this case, the multiplier M = 1/(1 - 0.6) = 1/0.4 = 2.5
An increase in government expenditure by X would increase the aggregate demand by 2.5X.
As the aim is to shift the aggregate demand curve to the right by $10 billion, the government should increase its expenditure by 10/2.5 = $4 billion.