Here's why:
* Gandora Dragon of Destruction's effect: It states "If this card is Normal or Special Summoned: You can target 1 monster on the field; destroy that target."
* Attacking after effects: In general, monsters can attack in the same turn they activate their effects unless the effect specifically states otherwise.
* No restriction: Gandora Dragon of Destruction's effect doesn't say anything about preventing it from attacking after using its effect.
Therefore, you can use Gandora Dragon of Destruction's effect to destroy a monster and then attack with it in the same turn.