Putting the information in a table makes it easier to solve. We’ll use 'H' for Haeduan, 'D' for Druidrider, T (true) for truth and F (false) for lying.
To begin with,
there aren’t any days where both of them told the truth and lied the day before, so we know one of them must be lying.
So we have two options, either 'Haeduan' is lying or 'Druidrider' is.
Option 1. Haeduan is lying.
In order for this to be the case, he needs to be lying today and telling the truth yesterday, so we need two days in a row with T F. And if Druidrider is telling the truth, he would need two days with F T. That means we’re looking for two days that have:
Haeduan: T FDruidrider: F T
Option 2. Druidrider is lying.
This is just the reverse of the above, so we need to find:
Haeduan: F TDruidrider: T F
The only day that matches either of the two options is Thursday, and it’s option 2. Druidrider is the liar. So, the traveler asked them the question on 'Thursday'.