In addition to @fefe's answer, which correctly explains this very basic pronunciation rule, I'd suggest to search for videos in Standard Mandarin about 一举两得 and see how its pronunciation is invariably yìjúliǎngdé.
Example 1
(His pronunciation is yìjúliǎngdé, 4-2-3h-2)
In the video, the man repeats 一举两得 four times. For your convenience, I cut out those small portions of audio. You can listen to the first occurrence clicking on the following link:
一举两得 in video 1
To make it even easier, I further cut only the portion 举两:
举两 in video 1
Example 2
(Her pronunciation is yìjúliǎngdé, 4-2-3h-2)
In this video, the woman repeats 一举两得 five times. As I did for the previous video, for your convenience I cut out these small portions of audio. You can listen to the first occurrence clicking on the following link:
一举两得 in video 2
And it should be easier to get it with the help of the following further cut of 举两:
举两 in video 2
Example 3
(Her pronunciation is yìjúliǎngdé, 4-2-3h-2)
In this last video, the woman repeats 一举两得 eight times. As with the previous videos, click here for 一举两得 in video 3 and here for 举两 in video 3.
Exercise
举
The last video is great because she pronounces 举 in three different ways (click on the links and listen to her different pronunciations, then try to repeat):
举 alone at 00:16, 上声, third tone:
举3
举 in 举动 at 00:18, 半上声, half third tone:
举3h
举 in 一举两得 at 00:08, 阳平, second tone:
举2
Besides, I put all three 举 in succession (third, half-third, and second tone) to make clear the difference. Listen to it here:
举3-3h-2
举两
Let's listen now to 举两 using the three different pronunciations of 举 (I've used the same pieces of 举 audio of the previous paragraph):
举两3-3h (don't repeat it :-)
举两3h-3h (don't repeat it :-)
Do you want to compare them with the correct one 举两2-3h? Here they are:
举两3-3h 举两2-3h
举两3h-3h 举两2-3h
一举两得
Do you wonder what the pronunciation of 一举两得 would be if 举 were in the third or half-third tone? Click the following links and try not to repeat! Note that, again, I've used the same pieces of 举 audio of the paragraph above.
一举两得 4-3-3h-2
一举两得 4-3h-3h-2
The following is the correct one, that is what she actually says eight times:
一举两得 4-2-3h-2
Compare it with each of the mispronounced ones:
一举2两得 一举3两得
一举2两得 一举3h两得
Lastly, in the following audio file you can listen to all the three "versions" of 一举两得 in succession (4-2-3h-2, 4-3-3h-2, and 4-3h-3h-2):
一举2两得 一举3两得 一举3h两得
P.S.: I would love to add some output from the tool suggested by @joehua. @joehua, can you help?