Answer
The statement is true.
Work Step by Step
Of 10,000 American adults:
$M$ is the set of all 315 tattooed Democratic men.
$W$ is the set of all 384 tattooed Democratic women.
$D$ is the set of all 699 tattooed Democrats.
A set of elements in $M$ and $W$ combined is a set of all 315 tattooed Democratic men and all 384 tattooed Democratic women, which means that it's a set of all $315+384=699$ tattooed Democrats.
The set of elements in $M$ and $W$ combined is equal to set $D$.
