As others have posted, the focal length doesn't change, but the field of view does.

I expect though that what you are asking is different from what you want to find out. I expect that you are really trying to determine something about equivalencies. Guess what - you will find that a 150mm lens for 6x4.5 is equivalent to ... a 150mm lens for 35mm.

You can work it out as follows (this is a very rough calculation).

It may be easiest to look at angles of view. The 150mm lens has a 26 degree angle of view on 6x4.5 film. The diagonal of 6x4.5 is about 75mm.

The 35mm frame has a diagonal of about 43mm.

So of those 26 degrees covered by the 150mm lens, about 43/75 x 26 = 15 degrees are captured by the 35mm frame.

What lens for 35mm format covers about 15 degrees? A 180mm lens covers 14 degrees, so that is close. A 150mm lens would be even closer .