f two dice are rolled once and one die rolled a second time if the...

Work backwards, then determine the probabilities
Explanation:
If the sum is 14, then possible values for the second roll (given that the first two are equal) and the value of the first rolls:
(First double, Second single)
${\displaystyle (6-6,2)}$
${\displaystyle (5-5,4)}$
${\displaystyle (4-4,6)}$
P(two 6's then a 2) ${\displaystyle ={\left(\frac{1}{6}\right)}^3=\frac{1}{216}}$
Same probability for the other two outcomes.
Total probability ${\displaystyle =\frac{3}{216}=\frac{1}{72}}$