Though Verna is supposedly light years away, the travel agent claims you can get there in a few seconds. What living situation does he use as an example to explain how it is possible?

The travel agent compares the proximity of Verna to Earth with the proximity of two apartment buildings. Building A has its entrance on Fifth Street, while Building B has its entrance on Sixth Street, but the buildings stand back-to-back. A couple living on the fourteenth floor of Building A (the Robinsons) and a couple living on the fourteenth floor of Building B (the Bradens) are actually only a few feet away from each other "as the crow flies"—if you drew a direct line between their living rooms, they are nearly close enough to touch each other.
However, due to the fact that the buildings' entrances open out in opposite directions onto different streets, these couples must travel a great distance to get to each other's living rooms. If the Robinsons want to visit the Bradens, they have to descend fourteen floors in an elevator just to get to street level, then walk all the way down their street, turn the corner, and walk all the way up the Bradens' street to get to the entrance to Building B. Once at Building B, the Robinsons must take another elevator to ascend fourteen floors to get to the Bradens' apartment. This journey is sufficiently long that "in bad weather [the Robinsons] have sometimes actually taken a cab."
The funny thing is that if the Robinsons could simply step through the walls of Building A and Building B, they could cross the actual physical distance between their living room and the Bradens's living room in a single stride. As the travel agent says:

" . . . if they could step through those two feet of wall without harming themselves or the wall—well, that is how we ‘travel.’ We don’t cross space, we avoid it.”

The distance between Earth and Verna is actually no distance at all, provided you travel in the correct "way," instead of going the long way.