Hint: Using the given data draw a diagram and use trigonometric ratios and Pythagoras theorem to obtain the solution.

Complete step-by-step answer:

In $\vartriangle ABC$

We apply pythagoras theorem to find out the length of string(AC)

$AC = \sqrt {A{B^2} + B{C^2}} $

$AC = \sqrt {{{(2.4)}^2} + {{(1.8)}^2}} $

$AC = \sqrt {5.76 + 3.24} $

$AC =\sqrt 9 = 3m $

Rate of pulling the string is $5cm/\sec$.

Length of string pulled in 12sec is $12 \times 5 = 60cm = 0.6m$

Now length of remaining string is $3 - 0.6 = 2.4m$

By pulling the string a new triangle is formed $\vartriangle ABD$.

$AD = 2.4m$ and $AB = 1.8m $

Now let's find BD by pythagoras theorem

$ BD = \sqrt {A{D^2} - A{B^2}} $

$ BD = \sqrt {{{(2.4)}^2} - {{(1.8)}^2}} $

$ BD = \sqrt {5.76 - 3.24} = \sqrt {2.52} = 1.58m $

$\therefore$ Horizontal distance of the fly from Nazinia after 12sec =1.58 + 1.2=1.78m.

Note: - In these types of questions always try to do with Pythagoras theorem and trigonometric ratio to find the unknown lengths.