Given radius r = 4 m.

The formula for the circumference of a circle is $C = 2\pi r$.
Given radius $r = 4$ m.

$$C = 2 \times \pi \times 4$$ $$C = 8\pi \text{ m}$$

The formula for the perimeter of a parallelogram is $P = 2(a+b)$, where $a$ and $b$ are the lengths of the adjacent sides.
Given sides are 6.51 m and $x$ m.

$$P = 2(6.51 + x) \text{ m}$$

Divide both sides by 2:

$$6.51 + x = \frac{8\pi}{2}$$ $$6.51 + x = 4\pi$$

Subtract 6.51 from both sides:

$$x = 4\pi - 6.51$$

Using the value of $\pi \approx 3.14159265...$:

$$x \approx 4 \times 3.14159265 - 6.51$$ $$x \approx 12.5663706 - 6.51$$ $$x \approx 6.0563706$$

Rounding to 2 decimal places, we look at the third decimal place. Since it is 6 (which is 5 or greater), we round up the second decimal place.

$$x \approx 6.06 \text{ m}$$

Thus, we have shown that $x = \boxed{\text{6.06 m}}$.