6. There is a batch of parts, with the smallest diameter being $12 \mathrm{~mm}$ and the largest being $12.5 \mathrm{~mm}$. If $x$ parts are randomly selected, there will always be 2 parts with a diameter difference less than $0.01 \mathrm{~mm}$, then the minimum value of $x$ is
6. 52

Divide a line segment between 12 to $12.5 \mathrm{~mm}$ into $n$ equal parts. If $n+1$ items are taken, then at least 2 items have a diameter difference that falls within the same equal part interval. From $\frac{12.5-12}{n} \leq 0.5$, we get the smallest $n=51$.