Just to get you started, you could read in the image and its GEOTIFF tags using the following command:
file = FILEPATH('boulder.tif', SUBDIR=['examples','data'])
data_variable=READ_TIFF(file, GEOTIFF=GeoKeys)
HELP, GeoKeys, /STRUCTURE
You would then need to pull apart the geotiff structure and write the data back to an HDF4 file. I don't quite understand why you need HDF4, and I'm also not sure how you're going to write the GEOTIFF data into the HDF4 file, since HDF4 doesn't have anything "specific" about map projections.
See the docs for more details:
http://www.harrisgeospatial.com/docs/read_tiff.html
Here's a really bad way to do the conversion:
https://www.hdfgroup.org/HDF5-FAQ.html#gtifftohdf
Basically, in that case you are only saving the image data, not the geotiff-specific data.
Good luck!