How can I wire up an quad channel amplifier to become stereo with 2 times the power?
No you can't

Compare the TDA7388 (4 x 45 W quad bridge car radio amplifier)

to the TDA7265 (25 +25W STEREO AMPLIFIER WITH MUTE &amp; ST-BY)

The TDA7256 can be used both as a stereo amplifier or a mono bridge amplifier. Note how the amplifiers basically have one output pin, the other side of the speaker is connected to ground.

Note how in the bridged configuration (page 11) the speaker is connected between the two amplifiers.

The TDA7388 also uses two pins connected to the speaker. There is no block diagram but I am quite sure it already uses two bridged amplifiers for each output, that's why it needs two pins to connect to each the speaker.

Also it runs on 12 V (as used in cars), the only way to get 45 W out of an amplifier running on 12 V is by using a bridged amplifier.

So the TDA7388 is already a bridged amplifier. There's no way to "double bridge" it.