Former Hagerstown Community College basketball coach Jim Brown was the top vote-getter on the Democrat side, with 3,598. He was followed by Commissioners Vice President Paul L. Swartz with 3,587 votes.
Other Democrats advancing are Commissioner Bert Iseminger with 3,497 votes, J. Herbert Hardin with 3,061 votes and Constance S. Cramer with 2,891 votes.
Thirteen Republicans and eight Democrats ran in the primary.
"I'm happy that I made it this far, and I'm going to keep doing what I'm doing," Snook said Tuesday night after the votes had been counted.
Snook said the current board of commissioners works as a team, which helped the incumbent commissioners advance.
Snook said he'll take a short break from campaigning, but plans to pick it up again in a few weeks.
Republican Doris J. Nipps, who has been a member of the Washington County Board of Education for eight years, said she was happy with her showing in the primary. She was the fourth highest GOP vote-getter.
"I'm very pleased," Nipps said. "I knew it would be difficult with all the folks running on the Republican side. Fourth is good. We'll just have to work a lot from now until November."
Hardin, a former public school educator and current School Board member, said he was pleased with the election results. Hardin was the fourth highest vote-getter on the Democrat side.
"I had told myself that if I was in this situation that I would be pleased, and I am," Hardin said.
"The first thing we have to do is sit down and talk about what we did right and what we did wrong," Hardin said.
He said he thinks the incumbents received such strong support in the primary because just 23 percent of registered voters cast ballots.
"I knew the incumbents would be re-elected when there wasn't a large number of citizens voting," Hardin said.
Cramer was afraid the low turnout would hurt her chances so she started collecting her campaign signs.
"I'm ecstatic," Cramer said. "I guess the people want their voice heard."
Cramer said she was optimistic about her chances in the general election.
Brown and Cramer both learned they made the cut by listening to the radio.
"All I can say is I'd like to thank the voters of Washington County who took the time to vote for me. I'm looking forward to working diligently to obtain a seat in the general election to serve them as commissioner," Brown said.
Brown and Cramer both said they would step up their campaigning.
Brown compared campaigning for the primary to a sports preseason.
"The primary gives you an opportunity to get the feel for what's going on and what the voters want. I'm hearing the voters loud and clear and I know what they want," Brown said.
Republican Paul H. Toothman, who lost his bid in the primary, said he plans to run again.
"I'll be back. We had a wide field of candidates this time," Toothman said. "I'm not going anywhere. I had a respectful showing and came in the middle of the pack."
Toothman received 1,714 votes.
Republican John C. Munson said he was happy with the results and that he hopes he'll receive support from both parties in November.
"I'm very happy about it," Munson said. "I think I did well. I just hope that the Republicans and Democrats will support me in the general election."
"I've been talking to some Democrats, and I know that a lot of them are going to vote for me in the general election," Munson said.
Munson said he ran in the primary for a spot on the board four years ago and lost by 11 votes. He said he plans to do more campaigning from now through November and is considering advertising on radio and television.
Staff writer Julie E. Greene contributed to this story.