Other answers cover techniques such as sizing and emphasis to draw the eye to a particular box, but, as you state, the boxes will all be stylisticly the same and they are not numbered (the numbers are there for us to pick out the ones we define as the most likely to view).
So instead I am going to justify my selection by refering to eye tracking studies.
It is probable with a grid of six boxes that are all equal and presented in a popup that takes centre stage and dims out the rest of the site, that a general, average user will jump around those six boxes with their eyes pretty quickly and it is difficult to say which boxes they will look at and in what order.
Firstly, we can discount typical eye tracking based on text websites, such as that defined in this article: http://www.nngroup.com/articles/f-shaped-pattern-reading-web-content/ - the popup nature means this is not like a normal website, the users focus is naturally drawn to a sinpler form in the centre of the screen by the
This article describes how the eye moves, actually flickering around quickly and taking in lots of points, moving from one to nearby, closely related items, however, the way the brain processes information in this rapid way means it does not always register everything in one go.
From the same blog, a summary of many eye tracking studies that shows users when presented with a new thing to look at will look at the centre first, then flick up to the top left, though the various heatmaps and histrogram studies in the article show a very dispersed set of orders of focus. They also describe how users move amongst content, fixation to fixation, though there is no stongly defined order
So, in conculsion, with a set of six boxes, centrally placed and all equal, the eye tracking studies and study of how the eye and brain work actually suggest that it isn't possible to define a strict order of precedence or even to say which box will be looked at first. We can also discount the top left fixation found with full websites as we are dealing with a popup and it is probable that the eyes will land on boxes 2 and 5 first, given the central nature of the popup.
I also think that the number of boxes will have an effect, if you had 20 instead of six I think things would be very different, but I have no evidence to back that statement up.
This is however a very specific case, you might even benefit doing your own eye tracking study and also benefit from real conversion data as to actually defining which box converts best