How do you build 4 equilateral triangles from 6 sticks? I've tried but the result is always the same! I can only get 3 equilateral triangles!...

Firstly, use all these sticks to make the edges of a tetrahedron figure.

Then, use three of the similar sticks to make a equilateral triangle.

Later, attack sticks to each  corner of the triangular face. Join them up, glue them together securely, so the sticks meet at their ends.

Presto, you create a tetrahedron, a pyramid with four faces, with four equilateral triangles with just six sticks.

An another easier method, too easy I say, is to follow what Croons 101 say, and just create a square with 4 of the sticks , and make other two sticks as diagonals of the square. Yoiu will still get the same result, but this method is not challenging enough.