Mesh analysis problem
I offer you first remember this in analyses :

1- write the Polarity of component which you enter it when you loop .
You're wrong in first loop is you write the 10v voltage source when you pass it 

2- the middle resistor have 2 current I1 &amp; I2 together . when you wanna write voltage of Common resistor between of two loop you should take positive (+) voltage for Intended loop and take  negative voltage  for which loop that your are not writing the equation for that ;



after this Ordered the equation you will have this 2 : 

I1:

4I1-2I2 = -10



I2:

4I2-2I1= +6

and sorry for my bad english and bad painting ;)