The D.C. Board of Elections and Ethics reversed itself yesterday and decided to guarantee delegate candidates pledged to President Carter a place on the May 6 District of Columbia primary ballot.

The board voted to dismiss challenges to the Carter slate in wards 1, 2, 6 and 8 filed by supporters of Lyndon LaRouche, a former U.S. Labor Party leader who is running for president as a Democrat.

Last week the board affirmed the challenges, rulling that the Carter campaign had misinterpreted the election code and that its slate of candidates for delegate to the Democratic National Convention was in danger of being kicked off the ballot in the four wards.

But the board ruled yesterday that the LaRouche supporters phrased their challenged documents improperly. The ruling had the effect of guaranteeing the Carter delegates slots on the ballot. The board also dismissed a similar LaRouche challenge to delegate candidates pledged to California Gov. Edmund G. (Jerry) Brown Jr.

The La Rouche supporters said they would appeal the board's decision to the D.C. Court of Appeals.

LaRouche backer Laura Chasen, who filed the challenges, said she had intended to question whether the Carter campaign complied with election laws requiring that delegate candidates collect 1,000 signatures in each of the city's two hypothetical "congressional districts" -- in particular, the district that includes wards 1, 2, 6 and 8.

But elections board members James L. Denson and Virginia P. Moye ruled that the papers filed by Chasen technically challenged only the right of Carter himself to appear on the ballot. That requires only 1,000 signatures citywide.