The 74153 (variants 74LS153, 74HC153) is a 74-series logic IC with two 4-input multiplexers sharing the same select lines.
.--\/--. /1E -> |01 16| -- +5V S1 -> |02 15| <- /2E 1I3 -> |03 14| <- S0 1I2 -> |04 13| <- 2I3 1I1 -> |05 12| <- 2I2 1I0 -> |06 11| <- 2I1 1Y <- |07 10| <- 2I0 Gnd -- |08 09| -> 2Y `------'
If /nE is high, then nY outputs low. Otherwise, nY copies the value of the pin nIx where x is chosen with S1 (msbit) and S0 (lsbit).
Many unlicensed multicarts used this IC as two independent one-of-two multiplexers via clever wiring of the inputs. If nI3 and nI2 are connected to one signal, and nI1 and nI0 are connected to another, then the output is selected by just the S1 pin. Similarly, if nI3 and nI1 are connected to one signal, and nI2 and nI0 are connected to another, then the output is selected by just the S0 pin.
Unlicensed multicarts almost always used this to select between H and V mirroring and between 16KiB and 32KiB PRG games.