Step 1: List what each concept means.
City Beautiful: an early twentieth century movement favouring grand civic architecture and formal, ordered layouts.
Conservative Surgery: a light-touch method of urban renewal that removes only the worst slum pockets and keeps the rest of the city fabric intact.
Happy City: the idea that the physical design of a city shapes the wellbeing and happiness of the people living in it.
Garden City: a planned town surrounded by a permanent belt of farmland and open land, meant to combine the advantages of the city and the countryside.
Step 2: Attach each concept to the person who introduced or is best known for it.
City Beautiful is linked to Daniel Burnham, through his role in the World's Columbian Exposition of 1893 and the 1909 Plan of Chicago.
Conservative Surgery is Patrick Geddes' own term, developed while he surveyed and advised on Indian towns in the early 1900s.
Happy City is the title and thesis of Charles Montgomery's 2013 book on urban design and wellbeing.
Garden City is Ebenezer Howard's proposal, published in 1898 and later built out at Letchworth and Welwyn.
Step 3: Rule out the leftover name.
Robert Owen belongs to an earlier generation of utopian reformers, known for the model industrial village of New Lanark, and is not the proponent of any of the four listed concepts here.
Step 4: Final match.
P - 2, Q - 3, R - 4, S - 5.
Final Answer:
$$ \boxed{\text{P - 2, Q - 3, R - 4, S - 5}} $$