Jack buys 2 * 8 = <<2*8=16>>16 polka dotted plates.
After smashing one, he has 4 - 1 = <<4-1=3>>3 flower plates left.
In total, he has 3 flower plates + 16 polka dotted plates + 8 checked plates = <<3+16+8=27>>27 plates.
#### 27