If theta is an acute angle of a right triangle and cos theta equals 3/8 what is the value of csc?

Trigonometry is based on a picture of a circle with the radius making an angle with the x axis. You carry this picture in your head, not your calculator. Trig is mostly imagination and the rest memorization.

Remember Chief SohCahToa
Sin = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent

Also memorize:
Sec = 1/Cos
Csc = 1/Sin
Cot = 1/Tan

Using the Pythagorean Theorem, you can generate a flood of identities. There is a list of some of them at en.wikipedia.org/wiki/List_of_trigonometric_identities and that is how you find solutions to such problems.

You want to use csc(Θ) = 1/sin(Θ), so you need to find the sine. sin(Θ) = ±√(1 - cos^2(Θ))