Sum 4 numbers, 1 bit each, with three full adders
Your solution is wrong. The output of your 1st FA is a+b. the output of your 2nd FA is LSB(a+b) + MSB(a+b) + c. Which is wrong.

Solution:
What we want is a+b+c+d. so produce the sum a+b+c using one FA. use second FA to add d with this sum. this will give the LSB of output. Adding carries of these FA's will give the MSB's. Use the 3rd FA to get the MSB's. See the figure given below.



A,B,C and D are the inputs.
Y2 is the MSB of output, Y0 the LSB and Y1 is the second LSB of output.