I need some help finding: the first local minimum point to the right of the y-axis of : y=1/2 sin(6(x-pie/4)+10

this is what i have done

A: 1/2

period: 2pie/6 = pie/3

vertical displacement: 10

max at 10.5 min at 9.5

i know the y is 9.5 and something gone weirdly wrong when i tired to find the x value.

period is pie/3 so divided by 4 to find the distance between two points = pie/12

then X= pie/3 - pie/12

X= pie/6 this is the correct answer on the answer key , i got it right.

further on, i tired to find the next point which is x,10. I minus pie/6 by pie/12..i got pie/6.

Help

how come i got another pie/6?..

Thank You