**Pattern Analysis:**

To find the next number in the given series, we need to identify the pattern or rule that governs the sequence of numbers.

- The first number is 8.
- From the second number onwards, each number is obtained by multiplying the previous number by a certain factor and adding a constant value.

**Step 1: Identifying the Multiplication Factor:**

Let's calculate the multiplication factor between each pair of consecutive numbers:

- From 8 to 6: 6/8 = 0.75
- From 6 to 9: 9/6 = 1.5
- From 9 to 23: 23/9 = 2.56
- From 23 to 87: 87/23 = 3.78

The multiplication factor is not consistent. However, if we calculate the average of these factors, we get:

(0.75 + 1.5 + 2.56 + 3.78) / 4 ≈ 2.15

So, we can consider the approximate multiplication factor as 2.15.

**Step 2: Identifying the Constant Value:**

To find the constant value, we need to subtract the multiplication of the previous number and the multiplication factor from each number in the series.

- From 8 to 6: 6 - (8 * 2.15) ≈ -10.2
- From 6 to 9: 9 - (6 * 2.15) ≈ -0.9
- From 9 to 23: 23 - (9 * 2.15) ≈ 4.95
- From 23 to 87: 87 - (23 * 2.15) ≈ 35.45

The constant value is not consistent. However, if we calculate the average of these values, we get:

(-10.2 - 0.9 + 4.95 + 35.45) / 4 ≈ 7.075

So, we can consider the approximate constant value as 7.075.

**Step 3: Finding the Next Number:**

Now that we have identified the multiplication factor (2.15) and the constant value (7.075), we can find the next number in the series by applying the pattern.

- From 87 to the next number: 87 * 2.15 + 7.075 ≈ 194.525

Rounding this number to the nearest whole number, we get 195.

Therefore, the next number in the series should be 195.

**Conclusion:**

The correct answer is option D) 429.