Though I have no idea where they got this number, the anti-gun crowd is crowing that 40% of guns are purchased at gun shows without background checks.
GEM found the source of that number. Discussion here
Unfortunately, that number has been co-opted by other "credible" sources
making it difficult to sort out. That "source" was used a cite in this
anti-document. If you look at both of them you see multiple problems. The anti-document says it's "fact", while the "source" says perhaps 40% yet provides no basis for that number.