What is m∠H?

Step 1: Recall all the theorems of the circle.
LINK: http://jwilson.coe.uga.edu/emt725/ReviewCir/ReviewCir.htm
Step 2: Note down given values and examine the figure
Step 3: Identify the suitable theorem for the given question.
NOTE: An angle inscribed in a semicircle is always a right angle.
EXAMPLE: In triangle ABC \angle C=90\degree
Step 4: Use the theorem to find the unknown value.
NOTE: The sum of the three interior angles is equal to 180.
EXAMPLE: From triangle ABC
\angle A+\angle B+\angle C=180\degree
46\degree + \angle B + 90\degree = 180
\angle B=180\degree-136\degree
\angle B = 34\degree