In its effort to debunk natural selection, Explore Evolution reiterates the debunked claims from the creationist book Icons of Evolution. That book claimed that textbooks misrepresented evolution by incorrectly characterizing certain popular experiments. Explore Evolution repeats the earlier book's arguments, reuses several of that books images without change (or attribution), and does not update its arguments to reflect more recent research.
The most fundamental error here is the claim that research on peppered moths and work on the Galápagos finches are the only, or at least major, examples offered for natural selection in textbooks. Those examples are frequently cited, but modern textbooks cite many other examples to show how natural selection works. Nor do modern textbooks cite those bodies of research for the purposes claimed in Explore Evolution. The treatment of natural selection in this book focuses exclusively on whether natural selection can generate biological novelty. That is an interesting topic, but not the only relevant topic for students to learn about natural selection, and Explore Evolution does students a disservice by treating an important and multi-faceted topic like natural selection through such a limited lens.
Turning to the details of the critiques offered for the peppered moth work and the Galápagos finch research, one finds that Explore Evolution describes that research inaccurately, and ignores recent work which directly contradicts the book's claims. For instance, it presents a graph of finch evolution which bears no relationship at all with any measurements reported by any researchers in the field, and criticizes the 50 year old work of Bernard Kettlewell on peppered moths without any discussion of research from the 1990s which tested several of the authors' criticisms of Kettlewell, and found that Kettlewell's results were unaltered by those criticisms.