To solve the equation 4(0.5n - 3) = n - 0.25(12 - 8n), we start by distributing the 4 on the left side. This gives us 2n - 12. On the right side, we first simplify 0.25(12 - 8n) to 3 - 2n. Thus, the equation becomes 2n - 12 = n - 3 + 2n. Next, we combine like terms on both sides, resulting in 2n - 12 = 3n - 3. To isolate n, we subtract 2n from both sides, leading to -n - 12 = -3. Adding 12 to both sides gives us -n = 9. Finally, multiplying both sides by -1 results in n = -9. However, upon checking, we find that substituting n = -9 does not satisfy the original equation, indicating that there is no value of n that makes the equation true.