First and Follow for the given grammar

Grammar:
$$\begin{array}{rcl} S &\to& aBDh\\ B &\to& cC\\ C &\to& bC \mid \epsilon\\ D &\to& EF\\ E &\to& g \mid \epsilon\\ F &\to& f \mid \epsilon \end{array}$$

Step 1 — FIRST sets

Compute allowed terminals that begin derivations (plus $\epsilon$ if nullable).

• $\mathrm{FIRST}(a) = \{a\},\ \mathrm{FIRST}(b)=\{b\},\ \mathrm{FIRST}(c)=\{c\},\ \mathrm{FIRST}(g)=\{g\},\ \mathrm{FIRST}(f)=\{f\},\ \mathrm{FIRST}(h)=\{h\}$
• $\mathrm{FIRST}(C) = \{b, \epsilon\}$ (from $C\to bC$ and $C\to\epsilon$)
• $\mathrm{FIRST}(E) = \{g, \epsilon\}$
• $\mathrm{FIRST}(F) = \{f, \epsilon\}$
• $\mathrm{FIRST}(D)$: $D\to EF$. FIRST(E)=$\{g,\epsilon\}$ → take $g$; since E nullable, take FIRST(F)=$\{f,\epsilon\}$ → $f$; since both nullable, include $\epsilon$.
  $$\mathrm{FIRST}(D) = \{g, f, \epsilon\}$$
• $\mathrm{FIRST}(B) = \{c\}$ (from $B\to cC$). (B is not nullable since $c$ is a terminal.)
• $\mathrm{FIRST}(S)$: $S\to aBDh$ → starts with terminal a.
  $$\mathrm{FIRST}(S) = \{a\}$$

Step 2 — FOLLOW sets

The follow of a nonterminal $X$ is the set of terminals that can appear immediately to the right of $X$ in some sentential form.

• $FOLLOW(S)$: S is the start symbol → ${$}$.
  $$\mathrm{FOLLOW}(S) = \{\$\}$$

• $FOLLOW(B)$: from $S\to a\,B\,D\,h$, after $B$ comes $D$, so we add $\mathrm{FIRST}(D)\setminus\{\epsilon\} = \{g,f\}$. Also $D$ is nullable, so we add $\mathrm{FOLLOW}(S) = {$}$.
  $$\mathrm{FOLLOW}(B) = \{g,\ f,\ \$\}$$

• $FOLLOW(C)$: from $B\to c\,C$ (C at the end), so $\mathrm{FOLLOW}(C) = \mathrm{FOLLOW}(B)$.
  $$\mathrm{FOLLOW}(C) = \{g,\ f,\ \$\}$$

• $FOLLOW(D)$: from $S\to aBD\,h$, after $D$ comes terminal h.
  $$\mathrm{FOLLOW}(D) = \{h\}$$

• $FOLLOW(E)$: from $D\to E\,F$, after $E$ comes $F$, so add $\mathrm{FIRST}(F)\setminus\{\epsilon\} = \{f\}$. Since $F$ is nullable, also add $\mathrm{FOLLOW}(D)=\{h\}$.
  $$\mathrm{FOLLOW}(E) = \{f,\ h\}$$

• $FOLLOW(F)$: from $D\to EF$ (F at the end), so $\mathrm{FOLLOW}(F) = \mathrm{FOLLOW}(D)$.
  $$\mathrm{FOLLOW}(F) = \{h\}$$

Final answer:
$${\small \mathrm{FIRST}(S)=\{a\},\quad \mathrm{FIRST}(B)=\{c\},\quad \mathrm{FIRST}(C)=\{b,\epsilon\},\quad \mathrm{FIRST}(D)=\{g,f,\epsilon\},\quad \mathrm{FIRST}(E)=\{g,\epsilon\},\quad \mathrm{FIRST}(F)=\{f,\epsilon\}}$$
$${\small \mathrm{FOLLOW}(S)=\{\$\},\quad\mathrm{FOLLOW}(B)=\{g,f,\$\},\quad\mathrm{FOLLOW}(C)=\{g,f,\$\},\quad\mathrm{FOLLOW}(D)=\{h\},\quad\mathrm{FOLLOW}(E)=\{f,h\},\quad\mathrm{FOLLOW}(F)=\{h\}}$$