Here are some examples which I have found in genuine Chinese textbooks and material. They all have a measure word omitted for unknown reasons.
我把这()事儿忘了。
您觉得这()音乐怎么样?
第三()医院
这()书房干净吗?
亿光四()大产品
Here are some examples which I have found in genuine Chinese textbooks and material. They all have a measure word omitted for unknown reasons.
我把这()事儿忘了。
您觉得这()音乐怎么样?
第三()医院
这()书房干净吗?
亿光四()大产品
There are several cases here.
Exemplar 1, 2, 4 are colloquial and informal. In this case measure words are optional after 这.
In exemplar 3, 第X YY is a common pattern to name institutions in mainland China: 第一人民医院, 第九中学, 第二汽车厂, etc. This is a remnant of the scheduled economy.
In exemplar 5, X大YY is also a common pattern: 四大名著, 六大奇书, 三大改造, etc. It means the top X most prominent items of a category.
They all have a measure word omitted for unknown reasons.
Because they all pointed to a single specific event/item, which is equivalent to the English form of "this + a singular noun").
Singular Noun vs Plural Noun:
我把这(件)事儿忘了。vs 我把这幾件事儿忘了。
您觉得这(首)音乐怎么样? vs 您觉得这幾首音乐怎么样?
这(間)书房干净吗?vs 这些书房干净吗?
Other Cases:
陸軍第三()医院 - The Third Hospital of the Army. Here, "第三(The Third)" is part of the name that is meant to indicate its rank, and uniqueness, in the chain of hospitals operated by the Army. It does not quantify the hospitals as in "陸軍第三座医院" - "The third/number three hospital that operated by the Army."
亿光四()大产品 - the measure word is often omitted when the adjective "大" proceeds the noun to emphasize its outstanding quality/quantity, such as "江南四(個)大美女", "十(項/個)大建設, so does "亿光四(項/個)大产品. (Similarily, "亞洲四(個/條)小龍.)
Measure words are optional in Chinese for the most part.
我們把這(尾)魚清蒸來吃
這(個)人心懷不軌
小陳住在這(座)大廈3樓