Given:
x = 3 √8

To find the value of x * 2 1/x * 2, we need to simplify each part of the expression step by step.

Step 1: Simplify x:
x = 3 √8

The square root of 8 can be simplified as follows:
√8 = √(4 * 2) = √4 * √2 = 2 √2

Substituting this value back into x:
x = 3 * 2 √2

Simplifying further:
x = 6 √2

Step 2: Simplify x * 2:
Now, we need to find the value of x * 2. Let's substitute the value of x we found in step 1:
x * 2 = (6 √2) * 2

Multiplying the coefficients (6 * 2):
x * 2 = 12 √2

Step 3: Simplify 1/x * 2:
Next, we need to find the value of 1/x * 2. To do this, we first need to find the reciprocal of x.

The reciprocal of x is:
1/x = 1/(6 √2)

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator (6 √2):
1/x = (1/(6 √2)) * (2 √2/2 √2)

Simplifying the numerator:
1/x = 2 √2/(12 * 2)

Simplifying further:
1/x = √2/24

Now, we can multiply the value of 1/x by 2:
1/x * 2 = (√2/24) * 2

Simplifying:
1/x * 2 = √2/12

Final Answer:
So, x * 2 1/x * 2 is equal to 12 √2 * √2/12, which simplifies to 2.