"First score method 6-way" is a betting line that is exclusive to the game of American football (or Canadian football).
With the "First score method 6-way" line, you are picking which team will score first, AND by what method. A "first score method 6-way line" that for a Colts vs Titans game might look like this:
Indianapolis Colts
Touchdown, 3.40
Field Goal, 4.50
Any Other, 56.00
Tennessee Titans
Touchdown, 2.45
Field Goal, 5.00
Any Other, 56.00
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So, let's say that you think that the Titans will open up the scoring in the game by kicking a field goal.
The line on this happening is 5.00, so if you bet $100 on this and the Titans kick a field goal to open up the scoring in the game, you would receive $400 in profit.
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One quick note - the "any other" line would include safeties, which are good for two points in the NFL. Safeties are quite rare, which is why this line is 56.00.