The U.S. Synthetic Fuels Corp. announced yesterday that it will begin negotiations that could result in billions of dollars in federal assistance for two large, coal-based synthetic fuels projects in Breckinridge County, Ky., and Gillette, Wyo.

The awards will be a major test of the Synfuels Corp. because they will be the first that the corporation will make on its own. Earlier projects, including the aborted 48,000-barrel-a-day Colony oil shale project, were inherited from the Department of Energy.

In the face of Exxon Corp.'s abandonment of that project and a generally gloomy outlook for synthethic fuels because of lower oil prices, the Synfuels Corp. has painted itself as approaching new projects with extreme caution.

Chosen to move into the final phase of selection are the Breckinridge Project, operated by a partnership of Ashland Synthetic Fuels Inc. and Bechtel Petroleum Inc., and the Hampshire Energy Project, a joint venture of Kaneb Service Inc., Koppers Co., Metropolitan Life Insurance Co., Northwestern Mutual Life Insurance Co. and Standard Oil of Ohio (which is not requesting government assistance).

The Breckinridge project is designed to produce 25,000 barrels a day of various liquid fuels from coal beginning in 1988. The Hampshire project is supposed to produce 19,000 barrels a day of gasoine from coal beginning in 1986.

Two other projects failed to make it to the final phase: the First Colony peat-to-methanol project planned for Creswell, N.C., and the Calsyn heavy oil upgrading project located in West Pittsburg, Calif. A decision was deferred on a fifth project, a coal gasification project sponsored by Memphis Light, Gas and Water, which was given more time to come up with additional assurances about management and the extent of its private backing.

An environmental group that follows the synthetic fuels industry criticized the Synfuels Corp.'s choices yesterday. "In selecting Hampshire and Breckinridge, the SFC board committed nearly $5 billion to the largest, most expensive and most trouble-filled projects among the five finalists," said Robert Roach, director of the Environmental Policy Institute's synfuels assessment project. Roach said that the Hampshire project has not yet publicly identified its coal source and lacks permits that it needs.

Officials of the Synfuels Corp. said that no exact amount of assistance has yet been set and that government negotiators will be tough.