There are indeed some mistakes in that excerpt from Wolpert & Tickle. First of all, the blastoderm is not a syncytium, it is a cenocyte instead (have a look at my answer here). By the way, that's a wrong nomenclature used by all books on developmental biology I'm aware of... therefore, being so well established, that wrong nomenclature probably won't change anytime soon. We have to get used to it.
Back to the numbers:
The second mistake in that excerpt (also reproduced by most books on developmental biology) is the number of divisions: it's not 12, but 13. And that would give us 213, or 8192 nuclei. As you can see, that's more than the ubiquitous "6000" we see everywhere in the literature.
Now the question becomes inverted: what's the reason for the blastoderm having a smaller amount of nuclei compared to the expected number?
According to Miles et al. (2010), the number of nuclei depends on the size of the egg:
The number of nuclei at the cellular blastoderm stage also changed in response to selection, with large-egg selected lines having more than 1000 additional nuclei relative to small-egg lines. This increase in nuclear number in larger eggs does not scale with egg size, however, as nuclear density is inversely correlated with egg length. (emphasis mine)
And the most important part of that paper, which addresses your (now inverted) question:
After 13 mitotic divisions the maximum possible number of nuclei at the blastoderm stage is 213 or 8192 nuclei, considerably more than the classic value of ~6000 given in the literature (Zalokar and Erk 1976; Turner and Mahowald 1983). We found that cell number is not anywhere near constant at 6000 nuclei in the cycle 14 embryo, but rather is positively correlated with egg size. On average, our large-egg selected treatment had more than 1000 additional nuclei than the small-egg selected treatment, a difference that arose as a correlated response to selection for egg size. Yet, in comparing cell numbers in other (nonselected) lines and species, we conclude that cell number must not be entirely a consequence of egg size, but rather must itself be a genetically variable trait. For example, D. sechellia (mean cell number = 7448.7, some embryos approaching the 213 limit) and the Ind strain of D. melanogaster (mean cell number = 6569.1) have nearly non-overlapping distributions of cell number despite having almost identical egg length. (emphases mine)
213 (or 8192) is the upper limit when considering 13 divisions. The real number of nuclei is less than that and varies from blastoderm to blastoderm. The mechanical explanation for that smaller number is, probably, that some nuclei fail to divide.
Also, it's worth mentioning that, from the 14th cycle on, the divisions become asynchronous, that is, the nuclei do not divide at the same time: some of them divide faster and some of them divide slower, and the exponential 2n (where
n is the number of divisions) for the total number of nuclei doesn't apply anymore (because, at a given moment, you have several different values for
- Miles, C., Lott, S., Luengo Hendriks, C., Ludwig, M., Manu, Williams, C. and Kreitman, M. (2010). ARTIFICIAL SELECTION ON EGG SIZE PERTURBS EARLY PATTERN FORMATION IN DROSOPHILA MELANOGASTER. Evolution, 65(1), pp.33-42.