I'm just eye-balling it here, but here's the ballpark estimate I got.

The detergent box looks like it's about 10 cm × 5 cm × 5 cm, so 250 ml. Let's assume there's about 250 ml of detergent in there.

I'm assuming that 50 ml is what you would normally use for that amount of laundry. That 250 ml is about 250/50 = 5x the usual amount.

I'm assuming that the recommended amount of detergent scales linearly with water hardness. BTW water hardness is pretty complicated, since there are many compounds that can mess around with detergent. For simplicity's sake, I'm going to ignore all of that and the awful hardness scales, and go with CaCO3 concentration in mg/l.

Usually, you'll have about 60...120 mg/l of CaCO3, and that's when you would use something like 50 ml of detergent. This time, we're going with 5x that amount, so I'll assume that means the water hardness should be around 5x as much. That adds up to 60 mg/l * 5 = 300. The upper estimate would be about 600 mg/l. That's well above what would be considered very hard water. Probably more like brine or something.

I thought about sea water, but that has plenty of Na+1 ions, but this thing would require metals with a +2 charge, so Mg+2, and Ca+2 are the usual ones. I guess Fe+3 and Al+3 would do the trick too. Where would you get lots of those? Maybe OP is washing their clothes with the raffinate stream of some industrial leaching process. Just find and acidic process, use Ca(OH)2 to adjust the pH, and you'll get raffinate like that. You could also use the AMD (Acid Mine Drainage) of an abandoned copper mine. Alternatively, consider using the reject of a reverse osmosis desalination plant.

On the other hand, if the ground water passes straight through a massive limestone deposit, you should get plenty of Ca+2 in the water. I guess that's the natural way to get to a situation like this. So, basically like those mineral water springs in Germany.

Anyway, so if you're a sane person, you won't be using this kind of water for washing your laundry. If you're in a super tight spot and all you have is RO reject or AMD, you're not completely screwed since you can compensate by adding absurd amounts of detergent. Just be prepared scoop up heaps of soap scum from the washing machine afterwards.