We want h < 4

but h = 12t-5t^2

so 12t-5t^2 < 4

subtract 4 from both sides gives

12t- 5t^2 - 4 <0

Rearrange as -5t^2 +12t -4 <0

Now consider the graph of -5t^2 +12t -4 (where t is on the X axis)

because this is a quadratic equation with a negative coefficient to the squared term we can say it has an "n" shape

At the axis the graph has a value of zero

-5t^2 +12t -4 =0

Factorise

(-5t +2)(t-2)=0

so t=2/5 or t = 2

This tells us the graph cuts the axis at t=2/5 and t=2

And the graph is negative (-5t^2 +12t -4 <0) below the axis ,which because of the "n" shape is to the left of t=2/5 and to the right of t=2

so 2/5 > t > 2

Also t cannot be negative so 0=< t < 2/5 and t>2