If it's a bulky yarn then you should use hook size H and up. If it's thinner then stick to the smaller size hooks. If your hook is too small then the yarn will not fit on the hook and it may snag on the hook as your working.
that would be a size P crochet hook
You should use a size J/10 crochet hook for a project that requires a 6 mm crochet hook.
The recommended size of crochet hook for working with yarn that is 5mm thick is typically a 5mm crochet hook.
A 00 crochet hook is typically around 9.0 millimeters in size.
A 3mm crochet hook is halfway between a C and D size in US sizes.
The recommended size of crochet hook in the US for working with a 3mm yarn is typically a size C or D hook.
You should use a crochet hook that is labeled as 5.00 mm for the project.
For this project, you should use a size 6 yarn crochet hook.
it is best to use an H or I size hook
A 5.0mm would be an H-8 hook.
In UK sizes, a 2mm crochet hook is a 14, it doesn't not have a US size equivalent. Here is a chart with crochet hook conversions from metric to US to UK.
For medium weight yarn, a recommended size of crochet hook is usually between 5.5mm to 6.5mm.