The work functions satisfy WA:WB=1:2.
Let WA=W and WB=2W.
Using the photoelectric equation
KE=hν−W, we have KEA=6−W and KEB=6−2W.
Given the kinetic energy ratio KEBKEA=2.642, we get 6−2W6−W=2.642.
Solving: 6−W=2.642(6−2W) gives 6−W=15.852−5.284W
So 4.284W=9.852 and W=2.3 eV.
Thus WA=2.3 eV and WB=4.6 eV.