Explanation:

Let's analyze the pattern in the given number series: $4, 10, 18, 38, ?, 150$. We observe an alternating pattern involving multiplication and addition/subtraction: 1. From the first term to the second: $4 \times 2 + 2 = 10$. 2. From the second term to the third: $10 \times 2 - 2 = 18$. 3. From the third term to the fourth: $18 \times 2 + 2 = 38$. The pattern is consistently $(\times 2 + 2)$, then $(\times 2 - 2)$, and then $(\times 2 + 2)$ again. Following this alternating pattern, the next operation after $38 \times 2 + 2$ should be $(\times 2 - 2)$. 4. From the fourth term to the missing term (?): $38 \times 2 - 2 = 76 - 2 = 74$. So, the missing number is $74$. To confirm, let's apply the next step in the pattern to $74$: 5. From the missing term ($74$) to the last term ($150$): $74 \times 2 + 2 = 148 + 2 = 150$. This matches the given last term, confirming our pattern and the calculated missing number. Option (4) $74$ is the correct answer. Options (1) $86$, (2) $78$, and (3) $76$ do not conform to the established alternating arithmetic pattern.