We know that there are $5$ vowels and $21$ consonants in English alphabets.
Choosing two vowels out of $5$ would be done in \[^{5}{{C}_{2}}\] ways
Choosing $2$ consonants out of $21$ can be done in \[^{21}{{C}_{2}}\] ways
The total number of ways selecting $2$ vowels and $2$ consonants
\[^{5}{{C}_{2}}~\times {{~}^{21}}{{C}_{2}}\]
Each of these four letters can be arranged in four ways \[^{4}{{P}_{4}}\]
Total numbers of words that can be formed are
\[24\text{ }\times \text{ }2100\text{ }=\text{ }50400\]