The correct answer is option 2, which includes the reasons 2 and 3 only.

Option 1 suggests that the Industrial Revolution emerged due to locating the production process in the countryside. This is incorrect because the Industrial Revolution actually involved the shift from rural areas to urban areas, with the emergence of factories in cities.

Option 3 suggests that the Industrial Revolution emerged due to the growing role of merchant-capitalists in the production process. This is correct because the Industrial Revolution was fueled by the investments and innovations of wealthy merchants who financed and organized large-scale industrial production.

Option 4 suggests that the Industrial Revolution emerged only due to the declining of guilds because of non-farming production coming under a single roof (the factory). This is also incorrect because while the decline of guilds did contribute to the emergence of the Industrial Revolution, it was not the sole cause. In fact, the advent of factories and the concentration of production in a single location were significant factors in the decline of guilds.

Therefore, the correct answer is option 2, which correctly identifies the reasons 2 and 3 as the main factors behind the emergence of the Industrial Revolution in Europe.