Explanation

(c)
$|z + 4| \leq 3$ represents the interior and boundary of the circle with centre at (-4, 0) and radius=3. As -1 is an end point of a diameter of the circle, maximum possible value of $|z + 1|$ is 6
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Alternate
$|z + 1| = |z + 4 - 3| \leq |z + 4| + | - 3| \leq 6$
Hence, maximum value of $|z + 1|$ is 6