This looks like a lot of steps, but take it slow and I think it should make sense. Also, maybe I am wrong…I guess I worked backwards since the question was posted with the answer of $69,000.
The cancellation of debt is netted to determine A's gain. Thus, A has a gain of $9,000 (15,000 off the books – 6,000 assumption of B debt). A also pays cash of $4,000. Thus, the credits to A are: 50,000 basis of property off the books, 6,000 of B's debt onto the books, 4,000 of cash off the books, and 9,000 of gain recognized. Total credits are $69,000. Moving to the debit side…we know A got rid of $15,000 of debt, therefore, the last debit to get us to $69,000 is $54,000 of basis in new property for A.
As for B, since he doesn't get to recognize a gain (he took on more debt than he gave up, that's a loss…never recognized for like kind exchange) the calculation is simpler. His credit side is $60,000 of basis off the books, plus $15,000 of A debt assumed. Credits total $75,000. This leaves the debit side with a $6,000 of debt off the books, and a new basis “plug” of $69,000 to get us to the $75,000 balancing entry.