First step back and consider the possibilities given no knowledge whatsoever:

For each child the problem constrains to one of two possible sexes and one of seven possible days of birth.

2 * 7 = 14 possible sex/day combinations for a single child.

(2 * 7) * (2 * 7) = 196 possible sex/day combinations for a pairing of two children. To see why, you could write a program to enumerate all of them, starting with the pairing "Boy/Monday + Boy/Monday", then "Boy/Monday + Boy/Tuesday" and so on until you exhaust all possible options at "Girl/Sunday + Girl/Sunday". You'll see there are 196 options.

Now start applying the facts given to us: one of the children is born on a Tuesday (eliminate all possibilities which don't have at least one Tuesday child), and that child is a boy (eliminate all possibilities in which there is not a Tuesday child who is also a boy).

This leaves exactly 27 possible cases:

Boy/Sunday + Boy/Tuesday,

Boy/Monday + Boy/Tuesday,

Boy/Tuesday + Boy/Tuesday,

Boy/Wednesday + Boy/Tuesday,

Boy/Thursday + Boy/Tuesday,

Boy/Friday + Boy/Tuesday,

Boy/Saturday + Boy/Tuesday,

Girl/Sunday + Boy/Tuesday,

Girl/Monday + Boy/Tuesday,

Girl/Tuesday + Boy/Tuesday,

Girl/Wednesday + Boy/Tuesday,

Girl/Thursday + Boy/Tuesday,

Girl/Friday + Boy/Tuesday,

Girl/Saturday + Boy/Tuesday,

Boy/Tuesday + Boy/Sunday,

Boy/Tuesday + Boy/Monday,

Boy/Tuesday + Boy/Wednesday,

Boy/Tuesday + Boy/Thursday,

Boy/Tuesday + Boy/Friday,

Boy/Tuesday + Boy/Saturday,

Boy/Tuesday + Girl/Sunday,

Boy/Tuesday + Girl/Monday,

Boy/Tuesday + Girl/Tuesday,

Boy/Tuesday + Girl/Wednesday,

Boy/Tuesday + Girl/Thursday,

Boy/Tuesday + Girl/Friday,

Boy/Tuesday + Girl/Saturday

If you count, you'll see that of those 27, there are 13 with two boys and 14 with a boy and a girl. The probability of two boys, given that one child is a boy born on Tuesday, is thus 13/27.