Utility/trade question

The budget constraint (straight line) shows all the combinations that can be afforded by the individual. The Indifference curve shows preferences over those combinations. Where the indifference curve meets the budget constraint is dependent on personal preference, for example a persons ideal combination of two goods which he can afford. Don't get too hung up on why it is a particular number, it just demonstrates a preference and a question has to state some sort of starting combination.

In 4 when it is increased I suspect it is 4 because of a mathematical function over preferences, it is not determined by anything within the graph. Again, don't give it too much thought. Its just a graphical way of understanding how a budget function and a utility function can be combined, as it is not always that intuitive if you use mathematical formulas when learning.

Ok, fair enough, so the numbers in 3 are given and that's how i know where to draw a utility function. But how do I solve question 4 in that case? How do I know where to draw utility function? If home specializes in cars, then it produces 12 cars (point b) and how do I determine how many it will export?

For 4 I suspect the answer given is just an example an not necessarily the only one that would have been marked correctly. In the absence of any specific mathematical function, in most cases its safes just to choose a level sort of increase in both goods when the budget constraint shifts out.