$$Statement\ 1:\ 2^{\left(2x+2\right)}=64$$
$$2^{\left(2x+2\right)}=2^6$$
Equate indices;
$$2x+2=6$$
$$x=\frac{4}{2}=2$$
$$y=2^{\left(x+1\right)}\ where\ x=2$$
$$y=2^{\left(2+1\right)}\ =2^3=8$$
Therefore, y - x = 8 - 2 = 6. Statement 1 is SUFFICIENT.
$$Statement\ 2:\ y=2^{\left(2x-1\right)}$$
$$From\ the\ question\ stem,\ y=2^{\left(x+1\right)}$$
$$Therefore,\ 2^{\left(x+1\right)}=2^{\left(2x-1\right)}$$
Equate indices;
$$x+1=2x-1$$
$$x=2$$
$$y=2^{\left(x+1\right)}\ where\ x=2$$
$$y=2^{\left(2+1\right)}=2^3=8$$
Therefore, y-x = 8-2 = 6.
Statement 2 is SUFFICIENT.
Since each statement alone is SUFFICIENT, the correct answer is option D.
