When you balance the equation you want to make the number of elements on each side of the equation equal.
There are 2 chlorines (Cl) on the right side so to balance that on the left side you put a 2 in front of the HCl. Now there are 4 hydrogens on the left side so to balance that on the right side you put a 2 in front of the H2O.
Balanced equation: 2HCl (aq) + Sr(OH)2 (aq) --> SrCl2 (aq) + 2H2O (l)
Now that the equation is balanced we can find the net ionic equation. First, separate all the aqueous solutions into their ions and keep any solid (s), liquid (l) or gas (g) unchanged.
2H+(aq) + 2Cl-(aq) + Sr+(aq) + 2OH-(aq) --> Sr+(aq) + 2Cl-(aq)+ 2H2O (l)
Any ions that are the same on both sides of the equation get cancelled out. Therefore, the 2Cl-(aq) and Sr+(aq) on both sides get cancelled out. This leaves you with the net ionic equation:
2H+(aq) + 2OH-(aq) --> 2H2O(l)