\frac{\sqrt[3]{6859}}{\sqrt[4]{256}}\times \frac{2}{57}\times 168=?

The correct option is 28.

Let us solve the given mathematical expression step-by-step.

The given expression is:

$\frac{\sqrt[3]{6859}}{\sqrt[4]{256}}\times \frac{2}{57}\times 168$

Step 1: Simplify the radical terms (cube root and fourth root).
First, evaluate the cube root in the numerator:
Since ${19}^3=6859$, we have:
$\sqrt[3]{6859}=19$

Next, evaluate the fourth root in the denominator:
Since $4^4=256$, we have:
$\sqrt[4]{256}=4$

Step 2: Substitute these values back into the fraction.
The first fraction becomes:
$\frac{19}{4}$

Step 3: Perform the multiplication.
Substitute this back into the original expression:
$\frac{19}{4}\times \frac{2}{57}\times 168$

Simplify the product of the first two fractions:
$\frac{19\times 2}{4\times 57}$

Since $57=19\times 3$, we can cancel 19 in the numerator and denominator:
$\frac{2}{4\times 3}=\frac{2}{12}=\frac{1}{6}$

Step 4: Multiply by 168 to find the final answer.
$\frac{1}{6}\times 168=\frac{168}{6}=28$

Thus, the final answer is 28.