Although that part of the document is a bit patchy, Yes it clearly says "Poorhouse"
- The next bit which is less clear is "Craiglockhart"
Then there is an address in 29 Deans Row Bathgate, which is where they were living in 1915 when the father attested to join the army. Bathgate is in West Lothian.
I read it as Ethel was born in 1913 at the Craiglockhart Poorhouse, and the other two boys were born in Bathgate at Deans Row.
I am sure someone will come along in the next "shift" and give you more information, in the meanwhile there is the link I posted above to the poorhouse.