Let the side length of the square ABCD be 6, and rotate 30 degrees clockwise around point a to get the square aefg, where the side FG and BC intersect at h, and find the length of BH

Let the side length of the square ABCD be 6, and rotate 30 degrees clockwise around point a to get the square aefg, where the side FG and BC intersect at h, and find the length of BH

The intersection I of the extension line of AB and GF
AI=AG/cos30°
BI=AI-AB
BH=BI/tg30°
AG=AB=6
The rest is up to you