F6 is built from F, A, C and D. F is the root, A the major third, C the fifth and D the sixth.
String by string, low to high, it plays F, C, F, A, D and F. Of the six strings you play, three give F, the note that names the chord. The lowest and highest notes are both F, two octaves apart, on strings 6 and 1.
You play F6 with a barre at fret 1. Your hand covers three frets, from 1 to 3. There is one more position, starting at fret 1.
Change only string 2 in F6 and you have F. Inside F6 sits a complete Dm chord, made of F, A and D. Bb shares three positions with this shape.
F6 belongs to six keys. In F major it is the I6, in Bb major the V6 and in C major the IV6. The rest appear in the key list.