Keep this in mind, your supply is 24V x 40A = 960W

generally this should be more than enough to meet your needs most of the time, however that charger is capable of loads up to 1200W and the rule of thumb is get a supply that is rated 25% higher to account for charger inefficiency if you plan to max out the load on a charger... so 1200W + 25% = 1500W supply needed

It's still possible to use your 960W supply provided you do the math and set your charger to the appropriate amount of current so you don't overload your supply

So... 960W - 25% = 720W of max load you want to set on the charger to play it safe

How much is 720W?

Let's say you're charging 4 packs each with 4S packs roughly at 5000mAh each

That's 4S x 4.2V/cell x 5Ah = 84W/pack @ 1C (or 5A per port)

so 4 packs at 1C = 336W
if you bump up to 10A per port (roughly 2C) then that increases the load to 672W which is approaching the limit for your supply.