What value of x will make the given triangles congruent?

Because you're trying to make them congruent, equal the two expressions to each other. 

So, for #10 you would equal them so it would look like this. 
2x+2=5x-19

Then you would just go ahead and simplify

2x+2=5x-19
-2x     -2x

2= 3x -19
+19    +19

21=3x
---  
3     3

x=7

This means that x should be 7. You can check this just by plugging it in

2x+2
2(7)+2 = 16

5x-19
5(7)-19= 16

Same with #11.

x+8=3x-14
-x     -x

8=2x-14
+14   +14

22=2x
---  
2     2

x=11

Check. 

x+8
11+8= 19

3x-14
3(11) - 14 = 19