$X_1 ≥ 0\quad \to (1)$
$X_2 ≥ 0\quad \to (2)$
$X_1 + X_2 ≤ 10\quad \to (3)$
$2X_1 + 2X_2 ≥ 22 \quad \to(4)$
Now the equation $(4)$ can be written as
$X_1 + X_2 ≥ 11 \quad \to (5)$
Now, equations $(3)$ and $(5)$ cannot hold true together since $X_1 ≥ 0$ and $X_2 ≥ 0.$
Hence, system of inequalities can never be satisfied.
Answer A. $0$