Let's say I have $3$ DC lines input as $10 V (x A), 24 V (y A), 6 V (z A)$. Now I want to convert the output to say $16$ VDC at $k A$.
What kind of converter can I use?
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The Wikipedia pages I've linked you to will explain everything in more detail, but briefly, a linear regulator works by "burning off" the extra voltage in the form of heat through a resistor voltage divider or Zener diode and a buck converter works by quickly switching the load's access to the power supply. If you could imagine blinking a light on and off quickly, the average output is some dimmer value (lower voltage) than the input.
There is no passive boost converter for DC; this relies solely on switching activity to excite an electrical storage component (inductor or capacitor) with the goal of raising (boosting) the voltage to a higher value than the input voltage.
These systems exist on-a-chip, so you would have to set specific output current requirements and pick a voltage source to find the exact solution suitable for you; you can search Mouser or Digikey to find the exact parts once you set your requirements.