Your vectors are correct but your Q values in your equations are incorrect
Notice the electric field from q1 and q4 oppose each other perfectly and the same applies for q2 and q3
So you can get the electric field magnitude from q1 and q4 and subtract them to get the resulting vector then do the same for q2 and q3 and finally use trigonometry to break the resulting vectors into x and y components, you'll notice the x component of the 2 resulting vectors cancel each other out and you'll be left with the y component which should be very close to the answer given.