Solution:
Let us consider the expansion of (a+b)n.
(a+b)n = nC0 a^n b^0 + nC1 a^(n-1) b^1 + nC2 a^(n-2) b^2 + …+ nCn a^0 b^n

We know that the sum of the coefficients of (a+b)n is equal to 2nCn.
Therefore, 2nCn = 4096

Step 1: Finding the value of n
We need to find the value of n for which 2nCn = 4096.
We can start by trying out different values of n.

When n=4,
2nCn = 2(4)C(4) = 2 x 4!/4! x 4! = 2
This is clearly not equal to 4096.

When n=6,
2nCn = 2(6)C(6) = 2 x 6!/6! x 6! = 42
This is also not equal to 4096.

When n=8,
2nCn = 2(8)C(8) = 2 x 8!/8! x 8! = 1287
This is still not equal to 4096.

When n=10,
2nCn = 2(10)C(10) = 2 x 10!/10! x 10! = 184756
This is also not equal to 4096.

When n=12,
2nCn = 2(12)C(12) = 2 x 12!/12! x 12! = 167960
This is still not equal to 4096.

When n=14,
2nCn = 2(14)C(14) = 2 x 14!/14! x 14! = 9694845
This is also not equal to 4096.

When n=16,
2nCn = 2(16)C(16) = 2 x 16!/16! x 16! = 35357670
This is still not equal to 4096.

When n=18,
2nCn = 2(18)C(18) = 2 x 18!/18! x 18! = 817190544
This is also not equal to 4096.

When n=20,
2nCn = 2(20)C(20) = 2 x 20!/20! x 20! = 155117520
This is still not equal to 4096.

When n=22,
2nCn = 2(22)C(22) = 2 x 22!/22! x 22! = 2541868560
This is also not equal to 4096.

When n=24,
2nCn = 2(24)C(24) = 2 x 24!/24! x 24! = 35999795184
This is equal to 4096. Therefore, n=24.

Step 2: Finding the greatest coefficient
Now, we need to find the greatest coefficient in the expansion of