**Given Information:**
The displacement of a particle moving on a straight line is given by x = 16t - 2t².

**To Find:**
The distance traveled by the particle during the first 2 seconds (S1) and during the first 6 seconds (S2), and the value of 3S2/S1.

**Solution:**

**Calculating the Distance Traveled:**

To find the distance traveled, we need to determine the magnitude of the displacement. As displacement can be both positive or negative, we consider the magnitude to determine the distance traveled.

The magnitude of the displacement can be found by taking the absolute value of x:

|x| = |16t - 2t²|

For the given equation, the particle is moving on a straight line. Hence, the distance traveled will be the sum of the magnitudes of the displacement for each interval.

1. **Distance Traveled during the First 2 seconds (S1):**
To find the distance traveled during the first 2 seconds, we substitute t = 0 and t = 2 in the equation x = 16t - 2t².

For t = 0:
x = 16(0) - 2(0)² = 0

For t = 2:
x = 16(2) - 2(2)² = 32 - 8 = 24

The distance traveled during the first 2 seconds (S1) = |24 - 0| = 24 units.

2. **Distance Traveled during the First 6 seconds (S2):**
To find the distance traveled during the first 6 seconds, we substitute t = 0 and t = 6 in the equation x = 16t - 2t².

For t = 0:
x = 16(0) - 2(0)² = 0

For t = 6:
x = 16(6) - 2(6)² = 96 - 72 = 24

The distance traveled during the first 6 seconds (S2) = |24 - 0| = 24 units.

**Calculating 3S2/S1:**

To find 3S2/S1, we substitute the calculated values of S1 and S2 in the given expression:

3S2/S1 = 3(24)/24 = 3 units.

**Answer:**
The value of 3S2/S1 is 3 units.