Q:

How do you charge 400v battery packs from 120v outlets for EVs?

You need a higher voltage to let current flow.
So how is it that you can to charge those big battery packs from home outlets without any additional equipment?

A:

The additional equipment is onboard the EV in today's crop of electric cars. The charger is part of the vehicle, while the station, formally known as EVSE, Electric Vehicle Service Equipment, negotiates with the charger, "letting it know" the source voltage and confirming that no one will be electrocuted once the power is turned on.
My 220v EVSE is bolted to the wall and provides 40A current to the onboard vehicle charger, after the aforementioned negotiation. I also have a portable 110v EVSE carried in the cargo bay. It too, informs the onboard charger that there's electricity.
My recent charge took four hours and seven minutes on the 220v EVSE. The charging estimate indicated that it would be forty or fifty hours if I used the 110v EVSE. I get about 30 miles per hour on the 220v and about 7 miles per hour on the 110v unit. Somewhere my math is incorrect on the low power EVSE, but it's unimportant to the overall assessment.
In both cases, there is additional equipment. It's a matter of convenience and cost which is used. For people who do not have regular access at home, public EVSE units, both free and paid can be found, but this also represents additional equipment.
Only two of my early EVs required no additional equipment other than an electrical cord and standard 110v outlet.

