The partial lunar eclipse of June 4 2012 will be visible over east Asia, Australia, the Pacific, and the western Americas. The Moon will be about one third covered by the Earth's umbral shadow at maximum eclipse; the umbral magnitude is 0.376.
The partial eclipse will begin at 09:59:24 UT and end just over 2 hours later at 12:07:04 UT, with the moment of greatest eclipse at 11:03:16 UT. The penumbral phases of the eclipse begin at 08:46:33 UT and end at 13:19:58 UT; these will be visible over a slightly larger area, and will be relatively hard to see, but should be visible before and after the partial eclipse as a shading across the Moon.
More information on this eclipse may be found at Fred Espenak's site.
The following map shows the areas where the partial eclipse will be visible:

Visibility of the partial eclipse.
This map shows the position of the Moon (the cross in the centre) at the time of maximum eclipse. The darkened area sees the whole partial eclipse; the pink areas to the right see only the beginning; and the blue areas on the left see the end. The moment of maximum eclipse will be visible from the darker pink and blue areas, and the whole of the darkened area.
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Copyright (C) 1995-2005 Ian Cameron Smith.
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