Step 1: Understand the question.
We need the database model in which one child record can have many parent records.
Step 2: Look at the hierarchical model.
The hierarchical model uses a tree shape. Here a parent can have many children, but every child has only one parent. So it does not allow many parents.
Step 3: Look at the network model.
The network model uses a graph shape. In it, a child can be linked to several parents at the same time. This is exactly the many parent feature we want.
Step 4: Look at the relational model.
The relational model stores data in tables joined by keys. It does not directly use the parent child idea the question asks about.
Step 5: Look at the flat file model.
A flat file is just a single plain list with no parent child links at all.
Step 6: Conclude.
Only the network model lets a child have multiple parents. So the answer is option 2.
\[ \boxed{\text{Network model}} \]