Your question seems as if it should be easy to answer. It isn't without much more information. Washington's Sentence Reform Act created "determinate" sentencing and eliminated parole. The SRA is changed almost every legislative session. This results in different outcomes depending upon the sentencing date and what kind of priors the defendant has.
Residential Burglary is a level 4 offense. A 15-20 month sentence range means that the defendant has prior convictions (with no priors the range is 3-9 months). A sentence within the standard range is the time to be served. Good time calculations are complex due to numerous changes in the law. In general, Residential Burglary is eligible for up to 33% good time. This can be less if prior convictions were for certain crimes. DOC is also using a "risk" scoring form to determine each inmates risk level.
To get the maximum available good time you need to avoid infractions of prison rules, do recommended programing and have a release plan approved by DOC.
A defendant's attorney, having all of the needed specific information, is in the best position to answer questions about the possibilites for a particular defendant.
The Sentencing Guidelines manual is available online at: http://www.sgc.wa.gov/
DOC's good time (and other) rules are at: http://www.doc.wa.gov/family/offenderlife/default.asp
All of the above is intended for informational purposes only and does not create an attorney-client relationship. The above answer is subject to modification depending upon an individual's particular circumstances.
A short answer would be that many prison sentences in Washington allow for one-third time off the sentence for good behavior. It is up to the Department of Corrections (which runs the state prisons) to calculate any good time credit. So, if the sentence ended up being 15 months, it is possible that a person would be released after 10 months.