ANSWER
Yes, (0,0) is a solution.
Step-by-step explanation
To check if (0,0) is a solution of this inequality we simply have to replace x by 0 and y by 0. If the inequality is true after replacing, then the point is a solution.
In this inequality we only have x,

0 is indeed greater than -4, thus this inequality is true and therefore (0, 0) is a solution