Let the first even number be 'x'

Then, second even number is (x+2)

And,   x(x+2)=6888

or       x²+2x=6888

⇒ x²+84x-82x-6888=0  [by splitting the middle term]

⇒ x(x-82)+84(x-82)=0

⇒ (x+84)(x-82)=0

⇒ x=82

and second number is 84.

∴ Greater number is 84.

Hence, Option E is correct.