Can I gank over at the same time as I go into a battlefield from my base for a showdown?

Yes, you can. You can simultaneously move units from your base and units with Ganking from another battlefield to the same destination.

According to Rule 144.3:

"Players may perform multiple Units' standard move simultaneously... When a Move like this is declared by a player, the units' Destination must be the same... the Origins do not need to be the same."

How it works:

1. Declare the Move: You choose the target battlefield as the destination for all units involved.
2. Select Units: You select the unit(s) at your base and the unit(s) with Ganking at your other battlefield.
3. Pay Costs: You exhaust all units involved in the move simultaneously (Rule 144.3.c).
4. Arrival: All units arrive at the destination at the same time. If this makes the battlefield contested, a single Showdown (or Combat, if opposing units are present) is triggered for the entire group (Rule 446.1).

As noted in RiftJudge FAQ #8465, Ganking is not a separate "special move" action; it is a passive ability that adds a new permission to a unit's Standard Move (Rule 810.1.c). Because both movements are legally performed as Standard Moves, they can be grouped into one simultaneous action.