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Here's what's really going on:

( b + 4c ) + ( 6b + 2c + 3d )

We gather up the like terms...

( b + 6b ) + ( 4c + 2c ) + 3d
                                                             This guy didn't have a partner.

And add the coefficients...

= 7b + 6c + 3d

Done!


TRY IT:

You have 4 bunnies, 2 piggies and 6 horsies...  Just kidding!

( 3x - 4w + z ) + ( 6x + 2w + 5z )


Now, look at this guy:

3x^2 - 5x + 7  (there is an x^2)   (there's an x guy)   ( there's a regular number guy)