The woman is a carrier for this lethal gene, so lets call her X'X (X' = lethal gene). Ok so the X'X woman is crossed with a normal male XY ( we assume hes normal because they didnt specify in the problem what is he).
X'X crossed with XY. To get 6 children, we have to do cross twice, since one cross only produces 4 children.
Cross 1 will give us these children: X'X, X'Y, XX, XY
Cross 2 will give us these children: X'X, X'Y, XX, XY
yes they're the same!
Ok now look at the boys. There are 4 boys total, but two of the boys are X'Y.
They are carrying the lethal gene, so the woman wont even give birth to these two since they will be spontaneously aborted. The remainder are two normal boys XY.
Hope this helps.