This puzzle presents pairs of seemingly unrelated pairs of words intersecting at common letters. There doesn't seem to be much we can do with them, though the presentation as letter tiles implies they might want to be moved or rearranged in some way.
The key here is to notice that you can shift certain words in certain directions to create new words. This shifting entails pushing a vertical word up/down or a horizontal word left/right one space, changing the intersecting letter in the other word to a letter adjacent to it in the shifting word. For example, the word LORES in the first pair can be shifted down one space to turn BOINK into BLINK, or up to turn it into BRINK.
You can continue the process from here, shifting either word until there are no more new words to make. Continuing from BLINK/LORES, we can shift the BLINK rightwards to make BORES, or from BRINK/LORES we can do the same thing to make LOBES. At this point there are no more possible common words that can be made by single-space shifts.
All that remains is to extract an answer somehow from these series of movements per pair. One of the most natural extrapolations is to keep a record of the directions shifted and try drawing these directions from a common point on paper. In our BOINK/LORES example, we'd draw up and then right from the point for one of the branches, and down and then right for the other - drawing out a crude C as seen in the top-left position below. You can click these images to get a closer look at the individual stages.
Repeating this for all pairs traces out the phrase CHAIN SHIFT, which is our answer. A "chain shift" in linguistics describes the change from one sound in a word to another over time, which is sort of what we've been doing here, as well as simply chaining together different-direction shifts.
|The answer is: chainshift|