The circumference of a circle with a radius of $4 \, \text{cm}$ is given by the expression $8\pi \, \text{cm}$.

To determine the circumference of a circle, we use the formula:

$C = 2\pi r$

where $C$ denotes the circumference and $r$ represents the radius of the circle. In this scenario, the radius $r$ is specified as $4 \, \text{cm}$. Substituting this value into the formula yields:

$C = 2\pi \times 4$

This expression simplifies to:

$C = 8\pi$

Thus, the circumference of the circle is $8\pi \, \text{cm}$.

If you require a numerical approximation, you can use $\pi \approx 3.14$ (though for greater accuracy, utilizing a calculator for the value of $\pi$ is recommended). Using this approximation:

$C \approx 8 \times 3.14 = 25.12 \, \text{cm}$

Therefore, the circumference is approximately $25.12 \, \text{cm}$ when $\pi$ is rounded to $3.14$. However, in most GCSE Mathematics problems, it is preferable to present your answer in terms of $\pi$, unless otherwise directed. This approach not only simplifies calculations but also enhances precision. Consequently, the exact circumference remains $8\pi \, \text{cm}$.