Consider the page from the book by Adamek & Rosicky: Locally presentable and accessible categories. given below. I need to derive this: Here is the statement
(2) to prove the universal property of $f$, it is sufficient to show that for each $\lambda-$presentable object $H$, each morphism $h:H\to B$ merging $p$ and $q$ factorizes uniquely through $f$.We know that $f$ factorizes through some $b_i$, say $h=b_i\cdot h'$. Then $$d_i^*\cdot (p_i\cdot h')=p\cdot b_i\cdot h'.$$
And here is the ERRATA to that page from the book.