Answer
$a=\pm3$
Work Step by Step
$f(g(x))=f(3x+a)=2(3x+a)^2+5=2(9x^2+6ax+a^2)+5$
The fact that it crosses the y-axis at $23$ means that $f(g(0))=23$.
Hence here $2(9\cdot0^2+6a\cdot0+a^2)+5=23\\2a^2=18\\a^2=9\\a=\pm3$
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