Another way of doing this is doing the same task with both versions of the page with the same participant, BUT ensure that you mix the order in which you display the designs. This is to minimise any bias.
Participant 1 will see Design 1, and then Design 2.
Participant 2 will see Design 2, and then Design 1.
Participant 3 will see Design 2, and then Design 1.
You want to be testing how well a participant can complete the task, rather than asking their opinions on which one they may prefer.
Also, consider running a series of small testing sessions, so you can iterate on the designs and keeping testing, rather than just the once off session with 6 participants.
Hope this helps.