REFERENCE wing area does not (should not!) change with flap deployment - or anything else. It's purely a convenience ofr the purpose of non-dimensionalising forces.
So, using the equation for stall speed:
Vs = sqrt[ (2*nz*mass) / (rho * S * CLmax)]
for the first case (m=10000, nz=1, Vs=240) we get:
240 = sqrt[ (2*1*10000)/(rho*S*CLmax)
which means that
rho*S*CLmax = (2*1*10000)/240*240 = 0.3472
Now, for the second cased we're told that CLmax has doubled in the landing config, so now we'll use rho*S*CLmax=0.6944
We also have mass=6400, and nz for a 30 degree bank is 1.155'g'
Therefore, we have:
Vs=sqrt [ (2*1.155*6400)/0.6944] = sqrt [21290] = 145.9
So the answer they want is 146
EDIT: I think the problem the last two posters have is that they are increasing stall speed by 15% for load factor.
In fact, the load factor for a 30 deg bank is 1.155'g' (1/cos30). That means the load factor is 15.5% above 1.0, so the stall speed increase for load factor is half that amount - 7.75%. If Airbus38 increases his 135.5 number by 7.75% he'll get 145.7. Which is, allowing for various roundings, the same as my answer.