ANSWER
The correct answer is C.
EXPLANATION
The given inequality is,
[tex]x + 2 \geqslant 6[/tex]
We add -2 to both sides of the inequation to get,
[tex]x + 2 + - 2 \geqslant 6 + - 2[/tex]
This implies that,
[tex]x + 2 - 2 \geqslant 6 - 2[/tex]
We simplify to get,
[tex]x \geqslant 4[/tex]
To illustrate this solution set on the number line, we draw an arrow pointing to the right, with the circle at the the boundary, which is 4 shaded or closed as shown in option C.
The correct answer is C.