Why is government interested in motivating producers of real goods?

Profit motive. That`s just my opinion. If you are efficient and people want and are interested in buying your stuff, you can make a profit and be well off. If people don't like your stuff or other people can do it better, you will go out of business and fail. You need to do it in a way that people are willing to pay you for it.

Of course economics is more complex than that with things like monopolies, oligopolies, monopolistic competition, perfect competition, etc but all of which will affect your profit motive, strategies and profit curves but the previous paragraph is a simple basic answer.

What are the ways of achieving the intensive economic growth?

Economic growth is measured by an increase in gross domestic product, or GDP, which is defined as the combined value of all goods and services produced within a country in a year. Many forces contribute to economic growth; unfortunately, no one is 100% clear about what these forces are or how to put them into motion. If this information was known, the economy, spurred by these forces, could grow at a constant rate unencumbered by recessions and stagnation.

Politicians and economists are forever holding debates on the different ideas trotted out with the promise of being economic panaceas. Once an idea is on the table, interminable squabbling ensues over its merits and pitfalls. Measures taken to induce economic growth include infrastructure spending, deregulation, tax cuts and tax rebates.

What are the ways of achieving the extensive economic growth?

Economic growth is the increase in the amount of the goods and services produced by an economy over time. It is conventionally measured as the percent rate of increase in real gross domestic product, or real GDP. Growth is usually calculated in real terms, i.e. inflation-adjusted terms, in order to obviate the distorting effect of inflation on the price of the goods produced.

In economics, "economic growth" or "economic growth theory" typically refers to growth of potential output, i.e., production at "full employment", which is caused by growth in aggregate demand or observed output

.Extensive Economic Growth:
Economic growth is achieved by increasing number of production factors