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I'm was not sure what is meant by projective in this context.

As in the case of understanding spoken or written language, an enormous
amount of general knowledge is constantly mobilized in service of
this projective activity, which freely utilizes any and all relevant sensory
data available to it. (The Irreducible Mind, Kelly, et al, p.40)

As I explained in comment, just the previous para. makes clear what "projective activity" means. That's the process of our mind "projecting" its past models on sensory data to recognize them without having to pay attention to all the details. I quote the previous para. here:

A separate tradition dating back at least to Kant and the early Gestalt
theorists, and carried forward into the modern era by psychologists such
as Neisser (1 967, 1 976), has been sensitive to the presence of "top-down"
influences, both within and between sensory modalities. Although a few
perceptual subsystems (such as those that engender the Miiller-Lyer and
other incorrigible visual illusions) may be truly autonomous or "cognitively
impenetrable" in the sense of J. Fodor ( 1983), these seem to be isolated and
special cases. A very different overall picture of perceptual synthesis is currently
emerging in which top-down influences predominate. On this view
40􀆈Chapter 1
perceptual synthesis is achieved not from the input, but with its aid. This is
necessarily the case for example in regard to ambiguous figures, where the
stimulus information itself is not sufficient to determine a uniquely "correct"
interpretation. More generally, we routinely ignore information that
is present in the input and supply information that is not, speed-reading
providing a characteristic example.29 Something within us, a sort of cosmogenic,
world-generating, or virtual-reality system, is continuously updating
and projecting an overall model of the perceptual environment and our position
within it, guided by very limited samplings of the available sensory
information (Simons & Chabris, 1999; Tart, 1993).

As I surmised, it's referring to what in psychology are referred to as projective tests. Here is the Wikipedia article to it if you want to know all about it. Link.

In a nutshell, projective tests present a subject with ambiguous stimuli, and a person is encouraged to tell the therapist or experimenter what has come to mind, or sometimes they are shown pictures and told to make up a story. The point of this is to try (not sure how successful it is) to get an idea of either unconscious processes or thoughts, or to understand a person's prior experiences.

Examples of these tests are ones like the ink blot tests, like Rorschach, Draw a Person Test, Sentence completion tests, and Thematic Apperception Test. The final one listed actually includes the word that psychologists and philosophers use, to apperceive.

1. to be aware of perceiving
   
   


2. (Psychology) psychol to comprehend by assimilating (a perception) to ideas already in the mind
   Collins English Dictionary
   

To give just a basic layman's explanation, as I am very lay, a person is said to perceive a stimulus. To say that a person "apperceives" something is to say that that person is perceiving the stimulus in the normal sense, but taking into consideration the totality of prior life experience and the prism through which we view the world. That's to say that different people perceive the same objects and stimuli in different ways. That's the point, or the aim of these projective tests, to try to reveal something through these tasks where people are told to share what they perceive from an ambiguous thing.

You can tell this is what the author is referring to, because just before your excerpt they write:

On this view perceptual synthesis is achieved not from the input, but
with its aid. This is necessarily the case for example in regard to
ambiguous figures, where the stimulus information is not sufficient to
determine a uniquely "correct" interpretation.