"volume of "NH_4Cl "solution"=400mL=0.4L
"Strength of "NH_4Cl "solution"=1.5M
"volume of "NH_3 "solution"=600mL=0.6L
"Strength of "NH_3 "solution"=0.1M
"Total volume of buffer soln"=0.4+0.6=1L
"Strength of "NH_4Cl "in buffer soln"=(1.5xx0.4)/1M=0.6M
"Strength of "NH_3 "in buffer soln"=(0.1xx0.6)/1M=0.06M
For NH_3 the
K_b=1.8xx10^-5
=>pK_b=-log(1.8xx10^-5)=5-log1.8=4.74
Now by Henderson Hasselblach equation pOH of the buffer
pOH=pK_b+log([[NH_4Cl]]/[[NH_3]])
pOH=4.74+log((0.6M)/(0.06M))=4.74+1=5.74
So for the buffer solution
pH=14-pOH=14-5.74=10.26