Answers
Can you name the four countries in the world that have exactly three distinct coastlines on one landmass?
Canada, Saudi Arabia, Malaysia, France
Can you name the three countries in the world that have exactly four distinct coastlines on one landmass?
The United States of America, Morocco, Russia
Can you name the one country that has exactly six distinct coastlines on one landmass?
Spain
Explanations
One of the two countries with four distinct coastlines (by this definition) is
The United States of America.
The four coastlines (on one landmass) are:
Alaska, Point Roberts, the Pacific coast (Washington to California), the Atlantic coast (Maine to Texas).
If you count Great Salt Lake as fitting your definition of "major saltwater sea", you could even make a case for this being a 5-coastline country.
This makes the second 4-coastline country:
Morocco
The four coasts are:
1. West of Ceuta
2. Between Ceuta and Peñón de Vélez de la Gomera
3. Between Peñón de Vélez de la Gomera and Melilla
4. East of Melilla
(Melilla credit to kaine)
(Peñón de Vélez de la Gomera credit to eudes)
The final 4-coastline country is:
Russia
The coastlines are:
1. Black Sea
2. Pacific Ocean
3. Baltic Sea (Kaliningrad)
4. Baltic Sea (St Petersburg)
I don't include the occupied territory of the Crimean peninsula. That's still part of Ukraine, even if Russia has tanks rolling all over it.
The 6-coastline country:
Spain
The coastlines here are:
1. Atlantic Ocean (north shore)
2. Mediterranean Sea (East of Gibraltar)
3. Strait of Gibraltar (West of Gibraltar)
4. The coastline of Ceuta across the Strait on Morocco's coast
5. The coastline of Melilla (credit to kaine on this 5th coast) to the East of Ceuta on Morocco's coast
6. The coastline of Peñón de Vélez de la Gomera (credit to eudes on this 6th coast) on Morocco's coast
.... Those sneaky Spanish!!
The four three-coastline countries are:
1. Canada — Pacific Ocean, Boundary Bay, Atlantic/Arctic Ocean
2. Saudi Arabia — Red Sea, Persian Gulf (x2) (credit to Bailey M)
3. Malaysia — South China Sea (x3, split twice by Brunei) .. bonus+2 Malacca Strait split by Singapore (credit to kaine)
4. France — North shore, south shore (x2, split by Monte Carlo)
Previously, I had listed Germany as a three-coastline country, but I suspect that Szczecin Lagoon is counted as a continuous extension of the Baltic Sea.