Can I charge a 6 volt golf cart battery with 36 volt solar panel?

The current will be limited by the internal resistance of the panel. Transformers don't work with DC.

With those numbers, the current would probably be limited to somewhere in the 2-4 amp range. I don't know the size of the battery, but this would probably not harm it, as this is probably only a trickle charge.

However, most of the energy from the panel would be wasted under those conditions. the 136 watts winds up as 24 watts into the battery, the rest wasted as heat in the solar panel. In fact, the panel may not work well under those conditions, it may overheat.

A good charge controller (an electronic box) will adjust the output voltage and input voltage to maximize the transfer to the battery and also prevent overcharging.

edit: downstepper? interesting term. Actually it is a DC-DC converter that converts 24 to 12 volts. But the specs say the input can't go above 28 volts, so that is not the proper device, it would burn out. And it would damage the battery aksi, And you want an output tailored for charging a battery, not a fixed voltage.

Again, get a charge controller that is specified for your battery voltage and size. they present the proper load to the solar panel to get the most power out of it, and also control the battery charging to charge it at the proper rate.

Transformers don't work with DC power and putting 36-42 volts on a 6 volt battery will destroy it and maybe the local surroundings if it explodes

You can use it, wasting a lot of power, by putting in a resistor to drop the voltage.

Basically it is not a good match - you could put 6 batteries in series and charge them with this panel and there is not a good way to get 6VDC from 36VDC except by making and custom switching power supply that will run off the 36 and produce 6-8 volts for charging.

Create Home Solar Power - http://solarpower.siopu.com/?eQK