Answer
$a=\pm5$
Work Step by Step
If $f\circ g$ crosses the y-axis at $68$ that means that $(f\circ g)(0)=68.$
$g(0)=2(0)+a=0$. Thus $(f\circ g)(0)=f(g(0))=f(a)=3a^2-7=68.$
Solve the above equation to obtain: $3a^2-7=68\\3a^2=75\\a^2=25\\a=\pm5$
