It is given in the question that measurement of arc BY is 24 degree and AB is the diameter . Therefore  measurement of arc BYA is 180 degree. Hence measurement of arc YA is
[tex]=180-24=156 degree[/tex]
And angle YAC is double of angle YA . And since YA is 156 degree. So angle YAC is
[tex]=\frac{1}{2} (156) = 78 degree[/tex]
And that's the required answer .
