The least squares estimator for beta in matrix notation in connection to normal equations and orthogonal projection in linear algebra [duplicate]

Somebody posted this link here about DERIVATION OF THE LEAST SQUARES ESTIMATOR FOR BETA IN MATRIX NOTATION-(https://economictheoryblog.com/2015/02/19/ols_estimator/). My question is 'How does THE LEAST SQUARES ESTIMATOR FOR BETA IN MATRIX NOTATION relate to NORMAL EQUATIONS and ORTHOGONAL PROJECTION' I would love examples too with maybe n=6 and k=3