The problem that happens when different brands, sizes, or ages of batteries are mixed together into one battery pack is that their Voltage levels become unbalanced over time. When the Voltages of the individual batteries in a battery pack become unbalanced some of the batteries become overcharged, and other become undercharged. This imbalance of Voltage between the individual batteries increases every time the battery pack is discharged and recharged and causes the batteries to wear out faster than normal due to overcharging and undercharging of the individual batteries.
You could mix two new batteries with two used batteries for a short period of time, and then remove the two old batteries and add two new batteries to the pack as long as the Voltages of all four new batteries in the pack were equalized to the same Voltage before using them as a battery pack.
Equalizing the battery Voltages (making them all the same) could be done with a 12 Volt battery charger, or with something that will draw power from the batteries like a 12 Volt light bulb. The goal is to have all of the batteries in the pack be the exact same Voltage before making the battery pack. After the batteries are charged or discharged to the same Voltage, the batteries should sit for 10 or 15 minutes so their Voltage level settles before taking the final Voltage measurement and determining that all batteries have the same Voltage and can be made into a battery pack.