I have a 6 speed freewheel with a chain which says HG on it. Can I use a 7/8 speed quick link on my chain?
"HG" indicates that this is a Hyperglide chain, but it doesn't tell us how wide the chain is, which is the critical question to answer—Hyperglide is a Shimano technology used on drive systems with different numbers of gears. Although you have a 6-speed freewheel, you might not have a 6-speed chain, and outer chain widths are different depending on the number of speeds, although you can use (for example) a 7-speed chain on a 6-speed freewheel.
The safest thing to do would be to replace your chain so that you know exactly what you have (if you don't know when your chain was last replaced, it's overdue anyhow). You can also try fitting this master link, and if it works, it works. If it's a 6-speed chain, I don't think it will work.