Cut 2 potatoes into cubes; cook potato cubes and 1 teaspoon salt in boiling water to cover 15 minutes or until tender. Drain and mash with a potato masher; set aside.
Shred remaining 2 potatoes; press between layers of paper towels to remove excess water.
Combine mashed and shredded potatoes in a large bowl; stir in remaining 1 teaspoon salt, onions, and next 4 ingredients. Gradually add flour to form a soft dough; shape into 12 patties.
Fry patties, in batches, in hot oil in a large skillet over medium-high heat 6 to 7 minutes on each side or until golden brown. Drain on paper towels.