Hi Benito! The first thing you need to do is obtain the first order conditions of the two individuals. Then you must equal their Marginal Rates of Sustitution (UmgX/UmgY).
In this example, you have (X12/X11)=(X22/X21)
With some algebra you obtain X12= (X22/X21)*X11.
Then use the fact that X11+X21=10 and also for good two X12+X22=10
With more algebra you get (10-X11)*X12 = (10-X12)*X11, finally X11=X22.
So the Pareto Curve is X11=X22.
I do not think we can get the contract curve without some math program solver, but we can draw an Edgeworth Box.
The Contract Curve would be the subset of the Parecto curve where the some individual can improve his utility taking into account the initial endowments (4,6) and (6,4)
I hope someone else can check if I am right.