Divisors of the Positive Integer 84. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
All are possible proper subgroups excluding the size of 1 and 84 because they are trivial subgroups but here the question is asking, Largest possible proper subgroup possible is 42...
The size of the smallest proper subgroup of $G=2?$
Lagrange's theorem states that order of every subgroup of G, it must be the divisor of G.
So the largest subgroup will be 84 which is trivial, but in the question it is asking for the proper subgroup hence it will be 42.