I read the article "The Homological Theory of maximal cohen-macaulay approximations" wrote by Auslander and Buchweitz. In this article in Lemma 3.1 in category theory drew commutative diagram by two exact sequence 
$$0 \rightarrow Y_A \rightarrow X_A \rightarrow A \rightarrow 0$$
such that above exact sequence is  X-approximaion of $A$ and 
$$0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$$
and since 
$$Ext^1(C,X_A) \rightarrow Ext^1(C,A)$$ 
is an isomorphism, there exist an exact commutative diagram like:
[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/gu8qx.png

my question is how calculate $Z$?
is pull back or push out?
Can help me please?
thanks