Here's a rough drawing of the triangle:
Since the sum of the angle measures in a triangle is 180°...
m∠BCA = 180° - 54° - 52° = 74°
Now look at quadrilateral CDHE.
Since the sum of the angle measures in a quadrilateral is 360°...
m∠DHE = 360° - 74° - 90° - 90° = 106°
And since ∠DHE and ∠AHB are vertical angles, they have the same measure.
m∠AHB = m∠DHE = 106°
Here's a rough drawing of the triangle:
Since the sum of the angle measures in a triangle is 180°...
m∠BCA = 180° - 54° - 52° = 74°
Now look at quadrilateral CDHE.
Since the sum of the angle measures in a quadrilateral is 360°...
m∠DHE = 360° - 74° - 90° - 90° = 106°
And since ∠DHE and ∠AHB are vertical angles, they have the same measure.
m∠AHB = m∠DHE = 106°