Let x be an integer and x + 1 be the other integer.
So the product of those two must be 63.
That means:
x(x+1) = 63
x^2 + x = 63
x^2 + x - 63 = 0
There are no integer values that satisfy this equation, so this question has no solutions.
Now if the question was find 2 pairs of consecutive ODD integers, then there is a solution.
The solution is 7 and 9. Anyway, hope that helps!