The Houndoominite is not available in Pokémon X as it is exclusive to Pokémon Y.
In can be found on Route 16 (post game) near Roller Skaters Jet and Olle, in the same location the Manectite can be found in Pokémon X.
It will only appear between 8:00PM- 9:00PM, once Professor Sycamore has upgraded the player's Mega Ring at the Anistar Sundial.
Note: You will need strength to get it.
For more help and assistance check out this walkthrough.
Since your on Pokémon X you can only get the Houndoominite if you trade for a Pokémon holding the Houndoominite.