Bam has collected x coins.
It is given that Kate has collected 6 more than twice the number of coins Bam has collected so Kate has collected 2x+6 coins.
Total number of coins is 14 so the equation that models the situation is as follows:
[tex]\begin{gathered} x+2x+6=14 \\ 3x+6=14 \end{gathered}[/tex]The equation is 3x+6=14.