Hegemony of this kind is all about the capacity to "manufacture consent". Which kind of hegemony it is?

Soft power

The correct answer is Option 3 - Soft power

The concept of "manufacturing consent," is closely associated with the idea of soft power. Soft power is the ability to influence others through attraction and persuasion rather than coercion or force. It operates by shaping the preferences of others through various means such as culture, ideology, and diplomacy. "Manufacturing consent" typically involves the use of soft power mechanisms like propaganda, media manipulation, and public relations to shape public opinion and garner support for certain ideas or policies.

NCERT: Hegemony as Soft Power- It would be a mistake to see US hegemony in purely military and economic terms without considering the ideological or the cultural dimension of US hegemony. This third sense of hegemony is about the capacity to ‘manufacture consent’. Here, hegemony implies class ascendancy in the social, political and particularly ideological spheres.

Hegemony arises when the dominant class or country can win the consent of dominated classes, by persuading the dominated classes to view the world in a manner favourable to the ascendancy of the dominant class. Adapted to the field of world politics, this notion of hegemony suggests that a dominant power deploys not only military power but also ideological resources to shape the behaviour of competing and lesser powers. The behaviour of the weaker countries is influenced in ways that favour the interests of the most powerful country, in particular its desire to remain preeminent. Consent, in other words, goes hand-in-hand with, and is often more effective than, coercion.

The predominance of the US in the world today is based not only on its military power and economic prowess, but also on its cultural presence. Whether we choose to recognise the fact or not, all ideas of the good life and personal success, most of the dreams of individuals and societies across the globe, are dreams churned out by practices prevailing in twentieth-century America. America is the most seductive, and in this sense the most powerful, culture on earth. This attribute is called ‘soft power’: the ability to persuade rather than coerce. Over time we get so used to hegemony that we hardly notice it, any more than we notice the rivers, birds, and trees around us.