As question lack major information of pedigree i have attached it in this answer for better understanding.
Answer:
Condition A is autosomal recessive
Condition B is a X- linked recessive
Explanation
We analyze the pedigree by checking the mode of inheritance of each condition.
Question arises here that is conditions are dominant or recessive?
Explanation of arose question
As we know that the requirement for dominant condition is that an affected individual must have one affected parent.
While on the other hand, two healthy parents gave birth to affected child which means this condition is recessive. therefore, from the pedigree we get to know that Recessive condition is the case for both conditions A and condition B.
Another question arises here is the condition is X-linked of autosomal?
Explanation of arose question
As we know from the rules of genetics that if two healthy parents gave birth to affected daughter then it’s an autosomal recessive condition. From the pedigree we see that this is the actual case of condition A.
While on the other hand, if two healthy parents gave birth to affected son this condition will be X-linked. From the pedigree this is the case for condition B.