There is no way to accurately predict the lifespan of a mixed breed dog. One can look at the average lifespan of both parent's breeds, in order to create a rough estimate. In this case, that would be a Rat Terrier and a Beagle.
The Rat Terrier's average lifespan ranges from 13 to 18 years, with some living to the age of 23 years. The Beagle's average lifespan ranges from 12 to 15 years. There is no way to determine the lifespan of a mixed breed puppy, as life expectancy is determined by health and other environmental and natural influences.