The quadrilateral is inscribed in the circle which means every corner point (A,B,C,D) is on the circle. No part of the quadrilateral is outside the circle.
One property of inscribed quadrilaterals is that the opposite angles add to 180 degrees. So, A+C = 180 B+D = 180
We know that A = 64 B = 6x+4 C = 9x-1
Let's use angles A and C to find x A+C = 180 64+9x-1= 180 9x+63 = 180 9x+63-63 = 180-63 9x = 117 9x/9 = 117/9 x = 13
Which helps us find angle B B = 6x+4 B = 6*13+4 B = 78+4 B = 82 degrees
Then we can finally find angle D B+D = 180 82+D = 180 82+D-82 = 180-82 D = 98 degrees
